# XL: Formulas to Find the Log and Inverse Log of a Number

### Summary

Microsoft Excel has built-in functions to calculate the logarithm of a number with a specified base, the logarithm with base 10, and the natural logarithm. To calculate the inverse log of a number in the first two cases, raise the base to the power of the value returned by the particular logarithm function being used. To find the inverse natural log, use the EXP function.

You can use the formulas in the following table to perform logarithmic and inverse log operations:

`   Formula       Operation              Example            Result   ---------------------------------------------------------------------   =LOG(n,b)     Log base b of n        =LOG(8,2)          3   =(b)^(x)      Inverse log of the     =2^3               8                 number x, base b   =LOG10(n)     Log base 10 of n       =LOG10(100)        2   =10^(x)       Inverse log of the     =10^2              100                 number x, base 10   =LN(n)        Natural log of n       =LN(100)           4.6051702   =EXP(x)       Inverse natural        =EXP(4.6051702)    100                 log of the number x `
In the preceding table, n is a variable that is either a value or the address of a cell containing a value, b (in the first function) is the base with which the logarithm is calculated, and x is a variable representing the result of the log function being used.

NOTE: Unless a different value or cell address is specified, the default value for the base is 10.