# How to find logarithm base

The logarithm connects the three numbers, one of which is the foundation, and another - podlogarifmennym value, and the third - the result of calculating the logarithm. By definition, the logarithm determines the exponent, which is necessary to build a base, to obtain the original number. From the definition it follows that these three numbers can be related to another and operations of exponentiation and root extraction.

### You will need:

Windows or Internet access.

## Instruction how to find logarithm base

Step 1:

By the definition of the logarithm of the result of its computation is the indicator of the extent to which it is necessary to build a foundation. Accordingly, the base for calculating produce operation inverse exponentiation, that is, remove the root. If the substrate is denoted by x, podlogarifmennuyu variable - through a, and the number of a value of the logarithm to the base x - by n, then the identity logₓa = n implies the identity x = ⁿ√a.

Step 2:

From the previous step, it follows that for the calculation of the unknown logarithm base is necessary to know the number of which has been removed the log and the result of this operation. For example, if the original number was 729, and the logarithm of it is equal to six, for computing the logarithm base remove the 729 sixth root: ⁶√729 = 3. Conclusion: The base of the logarithm is equal to three.

Step 3:

For practical calculations when finding the base of the logarithm is convenient to use the calculator, built-in Google search engine. For example, knowing that the log was removed from the 14641 number, and the result of this operation is equal to four, go to the homepage search engine and type in a single text field, the query: 14641 ^ (1/4). Here, the "cap" ^ means exponentiation operation, a fractional figure in brackets makes the search engine calculator to make the inverse operation - removing the root. After sending the request to a Google server will make calculations and determine the desired ratio of the logarithm: 14,641 ^ (1/4) = 11.

Step 4:

The same can be done with the help of a calculator built into the operating system. The latest versions of the operating system for its call, just press Win key, type "ka" and press Enter. The desired function of the root extract is placed in a "reverse engineering" version of the program - use the keyboard shortcut Alt + 2 to switch it on. For example, from the previous step, enter the number 14641, click the button with the symbol ʸ√x, enter 4 and press Enter. The result will be the same (11).