LG V10 with dual screen and two selfie cameras

is the base 10 logarithm. In other words, the base 10 logarithm of b {\displaystyle b} is the solution to the equation 10 x = b . {\displaystyle 10^{x}=b.}

A real decimal logarithm of b {\displaystyle b} exists if b > 0 {\displaystyle b>0} (a complex decimal logarithm exists for all b ≠ 0 {\displaystyle b\neq 0} ). It is customary (ISO 31-11 specification) to denote it lg b {\displaystyle \lg \,b} . Examples:

lg 1 = 0 ; log 10 = 1 ; lg 100 = 2 {\displaystyle \lg \,1=0;\,\lg \,10=1;\,\lg \,100=2} lg 1000000 = 6 ; lg 0 , 1 = − 1 ; lg 0.001 = − 3 {\displaystyle \lg \,1000000=6;\,\lg \,0{,}1=-1;\,\lg \,0{,}001=-3}

In foreign literature, as well as on the keyboards of calculators, there are other notations for the decimal logarithm: log , Log , Log10 {\displaystyle \operatorname {log} ,\operatorname {Log} ,\operatorname {Log10} } , and it should be borne in mind that the first 2 options can also apply to the natural logarithm.

Algebraic properties

The following table assumes all values ​​are positive[1]:

There is an obvious generalization of the above formulas to the case where negative variables are allowed, for example:

lg ⁡ | xy | = lg ⁡ ( | x | ) + lg ⁡ ( | y | ) , {\displaystyle \lg |xy|=\lg(|x|)+\lg(|y|),} lg | xy | = lg ⁡ ( | x | ) − lg ⁡ ( | y | ) , {\displaystyle \lg \!\left|{\frac {x}{y}}\right|=\lg(|x|)-\ log(|y|),}

The formula for the logarithm of a product can be easily generalized to an arbitrary number of factors:

lg ⁡ ( x 1 x 2 … xn ) = lg ⁡ ( x 1 ) + lg ⁡ ( x 2 ) + ⋯ + lg ⁡ ( xn ) {\displaystyle \lg(x_{1}x_{2}\dots x_{ n})=\lg(x_{1})+\lg(x_{2})+\dots +\lg(x_{n})}

The properties described above explain why the use of logarithms (before the invention of calculators) greatly simplified calculations. For example, multi-digit numbers x, y {\displaystyle x,y} were multiplied using logarithmic tables[⇨] using the following algorithm:

1. Find the logarithms of the numbers x, y {\displaystyle x,y} in the tables.
2. Add these logarithms, obtaining (according to the first property) the logarithm of the product x ⋅ y {\displaystyle x\cdot y} .
3. Using the logarithm of the product, find the product itself in the tables.

Division, which without the help of logarithms is much more labor-intensive than multiplication, was performed using the same algorithm, only with the addition of logarithms replaced by subtraction. Exponentiation and root extraction were carried out similarly.

Relationship between decimal and natural logarithms[2]:

ln ⁡ x ≈ 2.302 59 lg ⁡ x ; lg ⁡ x ≈ 0.434 29 ln ⁡ x {\displaystyle \ln x\approx 2{,}30259\ \lg x;\quad \lg x\approx 0{,}43429\ \ln x}

The sign of the logarithm depends on the number being logarithmed: if it is greater than 1, the logarithm is positive, if it is between 0 and 1, then it is negative. Example:

log 0.012 = log ( 10 − 2 × 1 , 2 ) = − 2 + log 1 , 2 ≈ − 2 + 0.079 181 = − 1.920 819 {\displaystyle \lg \,0{,}012=\lg \,(10 ^{-2}\times 1{,}2)=-2+\lg \,1{,}2\approx -2+0{,}079181=-1{,}920819}

To unify actions with positive and negative logarithms, the latter have an integer part ( characteristic

) was underlined at the top:
log 0.012 ≈ − 2 + 0.079 181 = 2 ¯ , 079181 {\displaystyle \lg \,0{,}012\approx -2+0{,}079181={\bar {2}}{,} 079181}
The mantissa of the logarithm, selected from the tables, with this approach is always positive.

LG V10 with dual screen and two selfie cameras

LG V10 is a new smartphone introduced by LG on October 1, 2015, which became the first model of the new V-series. The manufacturer promised to show a new model that could in some way surpass the existing flagship LG G4, and in truth, the Koreans succeeded. The LG V10 smartphone really has something to brag about not only over its peers, but also over smartphones from other manufacturers. Judging by its dimensions and technical content, the model is a direct competitor to such phablets as the Galaxy Note 5 from Samsung and the iPhone 6S Plus from Apple.

The first trump card of the LV B10 was its original design, as well as new case materials. The phone's frame is called Dura Guard and is made of 316L stainless steel (jewelry steel), and the Dura Skin back cover is made of rubberized material, has an interesting texture and is resistant to scratches and damage. According to the manufacturer, the phone case has a protection class according to the MIL-STD-810G standard, which means resistance to falls from a height of up to one and a half meters, which was verified by a number of tests in the laboratory. The design is truly excellent! The smartphone will be sold in five colors: Space Black, Luxe White, Modern Beige, Ocean Blue and Opal Blue. The dimensions of the phablet are far from small - 159.6 x 79.3 x 8.6 mm and weight 192 grams.

At the top of the front there are two more features of the LG V10 – an additional display and a dual front camera. This 2.1-inch screen has a resolution of 1040 by 160 pixels and is designed to display various useful information, application launch buttons, widgets, and it has an always-on mode in which you won’t miss anything and can do without turning on the main screen. Moreover, such a display practically does not consume battery!

Another significant innovation is the presence of a fingerprint scanner in the LG V10, which we have not previously seen on the company’s smartphones. In general, its location is good and the first responsiveness tests passed perfectly.

Selfie lovers will appreciate the phablet, because it is equipped with two 5-megapixel cameras, which will allow you to take excellent wide-angle photos (120 degree coverage), and a special algorithm will ultimately combine two photos into one. You can also activate the Multi-view Recording function and shoot from different points using all three cameras, and then choose which video you like best.

The technical characteristics of the LG V10 correspond to its status: the model is equipped with a 5.7-inch QHD display (2560 by 1440 pixels with a density of 513ppi), a Snapdragon 808 chipset with a 6-core processor with a frequency of 1.5 GHz and Adreno 418 video, 4 GB of RAM LPDDR3 and 64 GB of internal memory, while there is a slot for microSD memory cards up to 2 terabytes. But the battery could have been larger - the smartphone received a removable 3000 mAh battery. Supports 4G LTE-A (Cat.6), Wi-Fi, Bluetooth 4.1, NFC and USB 2.0.

The 16-megapixel main camera with F/1.8 sensitivity allows you to shoot even in low-light conditions. The camera is equipped with an LED flash, laser autofocus, and OIS 2.0 optical stabilization.

LG V10 Specifications:

There is no data yet on the price and start date of LG V10 sales in Europe and the CIS countries, but it is known about an October release in Korea, and then in the USA, China, key countries in Latin America, the Middle East and Asia.

Decimal logarithm function

If we consider the logarithm number as a variable, we get the decimal logarithm function: y = log x. {\displaystyle y=\lg \,x.} It is defined for all x > 0. {\displaystyle x>0.} Range of values: E ( y ) = ( − ∞ ; + ∞ ) {\displaystyle E(y) =(-\infty ;+\infty )} . The graph of this curve is often called a logarithmic

[3].

The function is monotonically increasing, continuous, and differentiable wherever it is defined. The derivative for it is given by the formula:

ddx lg x = lg ex {\displaystyle {\frac {d}{dx}}\lg \,x={\frac {\lg \,e}{x}}}

The y-axis ( x = 0 ) {\displaystyle (x=0)} is a vertical asymptote because:

lim x → 0 + 0 lg x = − ∞ {\displaystyle \lim _{x\to 0+0}\lg \,x=-\infty }

Application

Logarithms to base 10 were widely used for calculations before the invention of compact electronic calculators in the 1970s. Like any other logarithms, they made it possible to greatly simplify and facilitate labor-intensive calculations, replacing multiplication with addition, and division with subtraction; Exponentiation and root extraction were similarly simplified. But decimal logarithms had an advantage over logarithms with a different base: the integer part of the logarithm of the number x {\displaystyle x} ( characteristic of the logarithm

) [ lg ⁡ x ] {\displaystyle [\lg x]} is easy to determine.

• If x ⩾ 1 {\displaystyle x\geqslant 1} , then [ lg ⁡ x ] {\displaystyle [\lg x]} is 1 less than the number of digits in the integer part of x {\displaystyle x} . For example, it is immediately obvious that lg ⁡ 345 {\displaystyle \lg 345} is in the interval ( 2 , 3 ) {\displaystyle (2,3)} .
• If 0 < x < 1 {\displaystyle 0 , then the nearest integer to lg ⁡ x {\displaystyle \lg x} is equal to the total number of zeros in x {\displaystyle x} before the first non-zero digit (including the zero before the decimal point), taken with a minus sign. For example, lg ⁡ 0.001 4 {\displaystyle \lg 0{,}0014} is in the interval ( − 3 , − 2 ) {\displaystyle (-3,-2)} .

In addition, when you move the decimal point in a number n {\displaystyle n} places, the value of the decimal logarithm of that number changes by n. {\displaystyle n.} For example:

lg ⁡ 8314 , 63 = lg ⁡ 8.314 63 + 3 {\displaystyle \lg 8314{,}63=\lg 8{,}31463+3}

It follows that to calculate decimal logarithms, it is enough to compile a table of logarithms for numbers in the range from 1 {\displaystyle 1} to 10 {\displaystyle 10} [4]. Such tables, starting from the 17th century, were produced in large quantities and served as an indispensable calculation tool for scientists and engineers.

Since the use of logarithms for calculations has almost ceased with the advent of computer technology, today the decimal logarithm has been largely replaced by the natural one[5].
It is preserved mainly in those mathematical models where it has historically taken root - for example, in the construction of logarithmic scales. Decimal logarithms for numbers of the form 5 × 10 n

Please note that all numbers given in the table have the same mantissa.[ clarify

]
Decimal logarithmic scale on a slide rule

Review of the LG X view Android smartphone: an original mid-level solution

Table of contents

• Introduction
• Specifications
• Packaging and equipment
• Appearance and design
• Display
• Hardware platform and performance
• Software and firmware
• Multimedia
• Wireless Interfaces and Communications
• File system
• Battery life
• Camera
• Comparison with competitors
• Conclusion
• Additional photo examples

Introduction

Few large companies would dare to risk profits for the sake of experimentation.
But this is absolutely not the case. The manufacturer strives hard for innovation and fresh solutions in the field of smartphone construction. What are such unique examples like LG G Flex 2, LG G5 SE and LG X cam worth? All of them are original and interesting to consider in their own way. Even though not everyone turned out perfect, the “pioneer” always gets the most, so everything is natural.

Not long ago we reviewed the LG V10, which differed from other smartphones in its additional screen and high-quality camera. Now we have a similar solution in the middle segment and its name is LG X view. Or LG X screen, if we are talking about the international version.

First, let's look at the technical specifications.

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Specifications LG X view

In terms of characteristics, this is a completely modern budget-level device. The price seems a little high, but if you remember what times are now and how much it is in terms of currency, then everything falls into place. In addition, the smartphone is officially supplied to the Russian Federation and is supported by the manufacturer, so there should be no problems with the warranty.

Packaging and equipment LG X view

As is the case with many other LG smartphones, the hero of the review arrived in our laboratory without packaging or delivery kit. There is no point in expecting any surprises here, since recently large manufacturers have been trying to reduce economic costs as much as possible, and there is no point in making the kit very rich.

Appearance and design of LG X view

LG X view is an example of the classic design of modern smartphones. Everything is familiar here.

The body is made of plastic, you can immediately feel it when you pick up the device. It should be noted that the device is quite lightweight - only 120 g.

The design is non-separable, the back panel is disguised as glass. The case resists torsion well, no extraneous sounds were noticed. In addition to black, the user can choose white and rose gold.

The arrangement of the elements is similar to that used in Apple smartphones. All connectors are located at the bottom, including a 3.5 mm output and a ringing speaker. There is a noise canceling microphone on top.

The volume keys are on the left, the screen lock button is on the right.

Alas, the SIM card tray is universal. Nano SIM card format.

The keys are inserted tightly into the body, the accuracy of the panels does not cause any complaints. There are some differences in material processing, but this is normal for this class of devices. The buttons are made of plastic.

From the front side we have a view of “two” displays. As with the V10, there is one oddly shaped screen with no jumper between them.

It is logical to assume that such a layout makes sense only if the front camera and sensors are located on the side of the small display. Otherwise, it would be easier to increase the entire screen diagonal or separate them completely. Alas, there is no LED event indicator here.

The rear camera module is very simple; it consists of a medium-sized lens and one LED as a flash.

The protective glass is covered with a border - a good solution.

The frames around the display are moderately thick. They do not cause discomfort, but the design of the LG X view cannot be called sophisticated either. But the margins under and above the screen were a pleasant surprise; they are thin and look good.

Story

Main article: History of logarithms

The first tables of decimal logarithms were published in 1617 by Oxford mathematics professor Henry Briggs for numbers from 1 to 1000, with eight (later fourteen) digits. Therefore, abroad, decimal logarithms are often called Briggs

.
But errors were discovered in these and subsequent editions of the tables. The first error-free edition based on the tables of Georg Vega (1783) appeared only in 1857 in Berlin (Bremiker tables, Carl Bremiker
)[6].

In Russia, the first tables of logarithms were published in 1703 with the participation of L. F. Magnitsky[7]. Several collections of tables of logarithms were published in the USSR[8]:

1. Bradis V. M.
   Four-digit mathematical tables. M.: Bustard, 2010, ISBN 978-5-358-07433-0. Bradis tables, published since 1921, were used in educational institutions and in engineering calculations that did not require great accuracy. They contained mantissas of decimal logarithms of numbers and trigonometric functions, natural logarithms, and some other useful calculation tools.
2. Vega G.
   Tables of seven-digit logarithms, 4th edition, M.: Nedra, 1971. Professional collection for precise calculations.

Specifications LG B8

Price of LG B8 To make it easier to draw further conclusions, we suggest that you familiarize yourself with the estimated prices for LG B8. The series consists of two models. As of mid-November, the price of LG OLED55B8PLA starts at 87,000 rubles. A model with a 65th diagonal LG OLED65B8PLA will cost from 173,000 rubles. At the beginning of the article it was mentioned that there are two more models OLED55B8SLC and OLED65B8SLC.

The prices for them are still unknown, but they differ only in the design of the stand. To make it clear how much the buyer wins by purchasing the LG B8, we present the prices of the LG C8 series. C8 models with a 55th diagonal cost from 115,000 rubles, and with a 65th diagonal - 190,000 rubles. As you can see, in any case the difference exceeds 20,000 rubles. We draw our own conclusions.

LG B8 Review Summary

In conclusion of the review of B8 from LG, let's summarize. The main advantage of the LG OLED55B8 model is its price-quality ratio. Those who are in search of a quality TV will immediately understand that for such a price it is rare to choose something good even among LED TVs. If there is an LCD TV that surpasses the quality of the TV being considered in this article, then it will cost much more.

The main disadvantage of the LG B8 is that the other OLED models of 2018 will have better image quality.
On the other hand, the difference of about $400 is quite significant for many buyers. So, if you can add this difference, then it is better to buy the LG OLED55C8, since the Sony AF8 will cost even more. LG B8 review2018-11-12T22:57:03+00:00 ultrahdLGTVsOLED55B8PLA is the cheapest OLED TV LG has ever made. This feature is one of the main ones for many fans who dream of purchasing an OLED TV. However, before choosing this TV, the buyer should know that unlike other LG OLED models of the last year, the OLED55B8PLA does not give the same...ultrahdultrahd AdministratorUltraHD

Literature

Theory of logarithms

• Vygodsky M. Ya.
  Handbook of elementary mathematics. - ed. 25th. - M.: Nauka, 1978. - ISBN 5-17-009554-6.
• Korn G., Korn T.
  Handbook of mathematics (for scientists and engineers). - M.: Nauka, 1973. - 720 p.
• Fikhtengolts G. M.
  Course of differential and integral calculus. - ed. 6th. - M.: Nauka, 1966. - 680 p.

History of logarithms

• Zaitsev V.V., Ryzhkov V.V., Skanavi M.I.
  Elementary mathematics. Repeat course. — Third edition, stereotypical. - M.: Nauka, 1976. - 591 p.
• Klein F.
  Elementary mathematics from a higher point of view. - M.: Nauka, 1987. - T. I. Arithmetic. Algebra. Analysis. — 432 p.
• Mathematics of the 17th century // History of mathematics / Edited by A. P. Yushkevich, in three volumes. - M.: Nauka, 1970. - T. II.
• Mathematics of the 18th century // History of mathematics / Edited by A. P. Yushkevich, in three volumes. - M.: Nauka, 1972. - T. III.
• Uspensky Ya. V.
  Essay on the history of logarithms. - Petrograd: Scientific publishing house, 1923. - 78 p.

LG B6

The 55-inch LG B6 is the industry's third OLED OLED display. OLED TVs have several advantages over LCD TVs, offering deep blacks, stunning sharpness and excellent viewing angles.

The LG B6 has all these benefits and more. It supports not one, but several high dynamic range (HDR) formats: standard HDR10 video, Ultra HD Premium and Dolby Vision. So why does it cost $1,000 less than the comparable LG E6? It doesn't support , doesn't boast an attractive design, doesn't have the new designer remote control, and doesn't have the rich sound of the more expensive model. Can you live with these compromises? We can.

Design

The panel is thinner than on the more expensive E6 model. The LG B6 still has all the connections you need for a home theater setup, including four HDMI connectors, an Ethernet port, and built-in Wi-Fi.

Performance

Some may point out that in terms of maximum brightness, OLEDs are not as bright as LCDs, but the brightness range from full black to maximum illumination blows away LCDs, which simply cannot go down to true black. And while there have been color concerns in the past, the latest LG OLEDs seem to have addressed the issue, producing respectable color accuracy charts.

This panel is supposed to be identical to the E6, but our tests showed that the LG B6 has less of a cooler color bias than the E6.

Watching 4K HDR programs on the LG B6 is a real pleasure. Whites, for example, look disturbingly clean compared to images on other TVs like Samsung's KS9000, which can make some white objects appear yellowish.

The LG E6 and B6 models are almost identical, but we noticed some differences, especially in the increase in HD content. The E6 (which costs about $1,000 more) didn't seem to have any problems with the conversion, but there were some glitches with the B6's display in Cinema mode. In scenes with very fast movement, such as the open chase scene in Skyfall, the LG B6 had some flickering issues, although this will not be noticeable to some viewers.

Audio

In its preset Cinema Sound mode, the LG B6's sound is perfectly balanced and quite clear.

Switching audio to Music mode almost drowns out the sounds. My advice: leave it in Cinema mode.

Interface

Fast and attractive, LG's unique smart TV interface - webOS - improves with every iteration. Along a series of brightly colored tabs at the bottom of the screen, WebOS includes support for major streaming services like Netflix, Amazon and Vudu, but doesn't have the extensive support that others like Android TV have.

Notes

1. Vygodsky M. Ya. Handbook of elementary mathematics, 1978, p. 187..
2. Vygodsky M. Ya. Handbook of elementary mathematics, 1978, p. 189..
3. Logarithmic function. // Mathematical encyclopedia (in 5 volumes). - M.: Soviet Encyclopedia, 1982. - T. 3.
4. Elementary Mathematics, 1976, p. 94-100.
5. Klein F. Elementary mathematics from a higher point of view, 1987, p. 406..
6. History of Mathematics, Volume II, 1970, p. 62..
7. Gnedenko B.V.
   Essays on the history of mathematics in Russia, 2nd edition.. - M.: KomKniga, 2005. - P. 66.. - 296 p. — ISBN 5-484-00123-4.
8. Logarithmic tables // Great Soviet Encyclopedia.