The logarithm connects among themselves three numbers, one of which is the basis, another - podlogarifmenny value, and the third - result of calculation of a logarithm. According to definition, the logarithm defines an exponent in which it is necessary to build the basis to receive initial number. From definition follows that these three numbers can be connected also by operations of exponentiation and extraction of a root.
It is required to you
- Windows OS or Internet access.
Instruction
1. By definition of a logarithm the exponent in which it is necessary to build the basis is result of its calculation. Proceeding from it, you make for calculation of the basis operation, the return to exponentiation, that is take a root. If the basis to designate through x, a podlogarifmenny variable - through a, and value of a logarithm of number a on the basis x - through n, then from identity of logₓa = n follows identity x = ⁿ√ a.
2. Follows from the previous step that for calculation of the unknown basis of a logarithm it is necessary to know number from which this logarithm and also result of this operation was taken. For example, if initial number was 729, and the logarithm from it is equal to the six, for calculation of the basis of a logarithm take from the 729th a root of the sixth degree: ⁶√ 729 = 3. Conclusion: the basis of a logarithm is equal to the three.
3. For practical calculations when finding the basis of a logarithm it is convenient to use the calculator who is built in the Google search engine. For example, knowing that the logarithm was taken from number 14641, and the result of this operation is equal to the four, pass to the homepage of the searcher and gather such inquiry in the only text field: 14641^(1/4). Here "cover" ^ means operation of exponentiation, and the fractional exponent in brackets forces the calculator of the searcher to make the return operation - extraction of a root. After sending request for the server of Google will make calculations and will define a logarithm indicator necessary to you: 14,641^(1/4) = 11.
4. Same it is possible to do also by means of the calculator which is built in the operating system. In the latests version of OS for his call it is enough to press the Win key, to gather and to press Enter. Function of extraction of a root necessary to you is placed in "engineering" version of the program - use a combination of the Alt keys + 2 for its inclusion. For an example from the previous step it is necessary to enter number 14641, to click on the button with a symbol ʸ√ x, to enter 4 and to press Enter. The result will be the same (11).