You will need

- Scientific calculator

Instruction

1

In the calculator, typically there is a function to calculate the natural logarithm, i.e. the logarithm of any number to base e. But from the properties of the logarithm and the rules of operations on them, you can calculate a logarithm on the calculator on any other basis. For this you need to apply the formula of transition from the basis e to the desired new base.

2

Taking into account the transition formula, perform the calculation of the logarithm of the number b for the base and on the calculator, storing the generated intermediate results in the memory device. To do this, first calculate the natural logarithm of the number a, which is the basis of your original logarithm. Click on the calculator press [MC] to clear the calculator memory. Then dial the number of the base and click on the function of the natural logarithm [ln].

3

Save the resulting value of the logarithm in memory using the button [M+]. Next, clean the window with the results for further calculations by pressing [C].

4

Calculate the natural logarithm of the number b defined in your source log. To do this, enter on the calculator sequence: first b, then [ln]. Get the logarithm of a given number, but on the basis of E.

5

Calculate the logarithm given base. To do this, divide the last, the value of the logarithm of b to the memory an intermediate value of the logarithm. Click: [/] and [MR]. On screen display the first calculated number. Perform division by pressing [=]. The calculator will give you the screen the value that is the logarithm of the given number a in base b.

# Advice 2 : How to calculate natural logarithm

**Logarithms**are used in solving those equations in mathematics and applied Sciences in which the unknowns are both exponents. Logarithm with a base equal to the constant e ("Euler's number", 2,718281828459045235360...) is called 'natural' and often is written as ln(x). It shows the degree to which you want to raise the constant e to obtain the number specified as the argument of the natural logarithm (x).

Instruction

1

Use a calculator to compute the natural logarithm. This can be, for example, a calculator of the basic set of programs of the Windows operating system. Link to run it hidden pretty deep in the main OS menu - open it by clicking on the "start" button, then open the Programs section, go to "Standard," and then in the section "Service" and finally click Calculator. It is possible instead of the mouse and the menu to use the keyboard and a dialogue run programs - press the key combination WIN + R, type calc (this is the name of the executable file of the calculator) and press Enter.

2

Switch the calculator interface to advanced mode allowing the computation of logarithms. By default it opens in "normal" form, but you need "engineering" or "scientific" (depending on the version of the OS). Open in the menu "View" and select the appropriate line.

3

Enter the argument of the natural logarithm which has to be calculated. This can be done with the keyboard or clicking the mouse buttons in the calculator interface on the screen.

4

Click the button labeled ln - the program will calculate the logarithm base e and show the result.

5

Use any of the online calculators as an alternative way to calculate the value of the natural logarithm. For example, those which are available at

*http://calc.org.ua*. Its interface is very simple - there is only one input field, where you should type in the value of the number a logarithm from which it is necessary to calculate. Among the buttons, find and click the one that says ln. The script of this calculator does not require sending data to the server and waits for a response, so the result of the calculation you will receive almost instantly. The only thing you have to consider a separator between the fractional and the integer part of the number entered here must be dot, not comma.# Advice 3 : 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.

Instruction

1

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.

2

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.

3

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.

4

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.

5

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).

6

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.

7

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.

8

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).

9

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).