Advice 1: How to calculate logarithm on a calculator

Logarithm number b for the base a is defined as a measure of the degree to which it is necessary to build a base a, to obtain the number b. As a rule, modern calculators allow you to calculate logarithms base 10 and e, that is, decimal (log) and natural (ln) logarithms , respectively.
How to calculate logarithm on a calculator
You will need
  • Calculator, basic knowledge in mathematics.
Check whether a calculator to count the logarithms. Typically, this can do the more advanced versions or engineering calculators. Very easy to find out whether a calculator to count the logarithms. If so, he has a button that says ln and log.
After you verify that the calculator allows to count the logarithms, enable it and enter the number whose logarithm you want to calculate. Suppose you want to find the decimal logarithm of the number 324. The digits on the calculator 324.
Then click on the "log" if you want to find the logarithm or the button "ln" - if it's real. After that, the calculator will calculate the and the screen shows the answer. In the example number 324 if you count the decimal logarithm, get answer 2.5104, and if natural, then 5.7807.
The logarithm of the number equal to or less than zero, there is no calculator in this case will give you an error.
Useful advice
Easy to mind can calculate the logarithm of a unit, he is always equal to 0, and logarithms, which are a power base. They will simply be equal to this degree.

Advice 2: How to calculate power of number

The degree numbers apart in school algebra lessons. In life, this operation is rarely performed. For example, when calculating the area of a square or volume of a cube is used because the length, width, and the cube, and height – equal values. Otherwise, exponentiation is most likely to be applied during the production.
Computing is best done on paper, not in mind.
You will need
  • Paper, pen, scientific calculator, table of degrees, software (e.g., spreadsheet Excel).
To calculate the degree number in mathematical language means to build any number to any degree. Suppose you want the number X raised to the power n.
For this, the number X multiplied by itself n times.
Let X = 125, and the degree of number, i.e. n = 3. This means that the number 125 you need to multiply on itself 3 times.
125^3 = 125*125*125 = 1 953 125
Another example.
3^4 = 3*3*3*3 = 81
When working with a negative number you need to be careful with the signs. It should be remembered that even the degree (n) yields a plus sign, odd – minus sign.
For example
(-7)^2 = (-7)*(-7) = 49
(-7)^3 = (-7)*(-7)*(-7) = 343
Zero degree (n = 0) from any number will always be equal to one.
15^0 = 1
(-6)^0 = 1
(1/3)^0 = 1if n = 1, the number to multiply with itself is not necessary.
7^1 = 7
329^1 = 329
The opposite of the construction of a number to a power is called the root.
If 5^2 = 25, the square root of 25 is 5.
If 5^3 = 125, then the root of the third degree is equal to 5.
If 8^4= 4 096, the fourth root of 4 096 will be equal to 8.
If n = 2, then the degree is called square if n = 3, the degree is called a cube. The calculation of square and cube of first ten numbers to produce quite easily. But with the increase in the numbererected in degree, and with increasing degree, the computations become time consuming. For such calculation we developed a special table. There are also special engineering and online calculators, software. As a simple software product for operations with degrees, you can use the table editor Excel.

Advice 3: How to calculate natural logarithm

Of the total number of logarithms of the two highlighted is the logarithm base 10 (decimal) and base equal to the number of "e" constant, which is called "Euler's number". This constant is an irrational number that is not exact value, but an infinite fraction. The logarithm of such a basis is called natural and has much more application in integral and differential terms than the logarithm.
How to calculate natural logarithm
Use the online calculators as the most rapid method of calculating natural logarithms if you have access to the Internet. Such services are quite a lot online, but look for them through search engines is not necessary - some of the search engines themselves have calculators for the desired function. For example, you can use the calculators search engines Google or Nigma. Going to home page of any of these systems, type in the search box write the desired mathematical operations. For example, to calculate the natural logarithm of the number 0,489 type "ln 0.489". The separator between integer and fractional parts it is better to use a period, although Nigma understand correctly and the number with a comma separator.
Use a software calculator that is built into the Windows operating system, if Internet access is missing. You can open it via the main menu on the "start" button (section "All programs", subsection "Standard", section "Service", select "Calculator") or using the run dialog programs which is called by the key combination WIN + R. In the dialog you can enter the command calc and click the "OK"button.
Switch a running calculator in the more advanced mode. If you are using Windows XP or earlier, the desired mode will be called "engineering", and later versions (Windows 7 and Windows Vista) is "scientific." Item with the same name in any version of OS is posted under the "View" menu of the calculator.
Use the keyboard or UI buttons on the screen to enter a number, the natural logarithm of which to calculate. Then click the button labeled ln and the program will calculate and show the calculation result.

Advice 4: How to find logarithm

Logarithm of number x to base a is called is the number y such that a^y = x. Since logarithms simplify many practical calculations, it is important to be able to use them.
How to find logarithm
The logarithm of a number x to the base a will be denoted by loga(x). For example, log2(8) — logarithm of 8 base 2. It is equal to 3 because 2^3 = 8.
The logarithm is defined only for positive numbers. Negative numbers and zero have no logarithms, regardless of base. Thus the logarithm can be any number.
The base of the logarithm can be any positive number except unity. However, in practice, most often uses two base. Logarithms base 10 are called decimal and denoted by lg(x). Decimal logarithms are most often found in practical calculations.
A second common base for logarithms is an irrational transcendental number e = 2,71828... the Logarithm base e is called natural and is denoted by ln(x). The functions e^x and ln(x) have special properties that are important for differential and integral calculus, so natural logarithms are often used in mathematical analysis.
The logarithm of the product of two numbers is equal to the sum of the logarithms of these numbers by the same base: loga(x*y) = loga(x) + loga(y). For example, log2(256) = log2(32) + log2(8) = 8.The private logarithm of two numbers is equal to the difference of their logarithms: loga(x/y) = loga(x) loga(y).
To find the logarithm of a number raised to a power, you need the logarithm of the number multiplied by the exponent: loga(x^n) = n*loga(x). In this case the exponent can be any number — positive, negative, zero, integer or fractional.Because x^0 = 1 for any x, loga(1) = 0 for any a.
The logarithm replaces the multiplication, addition, exponentiation, multiplication, and root extraction division. Therefore, in the absence of computing logarithmic tables significantly simplify the calculations.To find the logarithm of a number that is not in table, it needs to be represented as the product of two or more numbers, the logarithms of which are in the table and find the final result, adding these logarithms.
A fairly simple way to calculate the natural logarithm is to use the decomposition of this function into a power series:ln(1 + x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ... + ((-1)^(n + 1))*((x^n)/n).This row gives the values ln(1 + x) for -1 < x ≤1. In other words, it is possible to calculate the natural logarithms of the numbers from 0 to (but not including 0) to 2. Natural logarithms of numbers outside of this series is found by summing, using the fact that the logarithm of product is sum of logarithms. In particular ln(2x) = ln(x) + ln (2).
For practical calculations it is sometimes convenient to switch from natural logarithms to decimal. Any transition from one base of logarithm to another is according to the formula:logb(x) = loga(x)/loga(b).Thus, log10(x) = ln(x)/ln(10).
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