What is the relationship between exponent and logarithm?

The exponent says how many times to multiply a number.


25 = 32

The exponent here is 5.

The logarithm says what exponent was used to multiply a number in order to get another number.


log2(32) = 5

5 is the exponent that was used to multiply 2 to get 32.

Exponent and logarithm “undo” each other.

Exponent: Given the base 2 and the exponent 5, 2 is multiplied by itself 5 times, which produces 32.

Logarithm: Given the base 2 and the number 32, we get the number of times 2 was multiplied to itself to get 32, which is 5.

Comparing the graphs of the two functions, we can easily see that the graph of logarithm is the inverse of the graph of exponent.

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