Final answer:
Exponential and logarithmic functions are inverses of each other because they undo each other's operations.
Step-by-step explanation:
Exponential and logarithmic functions are inverses of each other because they undo each other's operations. An exponential function involves raising a base number to a power, while a logarithmic function involves finding the exponent to which a base number must be raised to equal a given number.
For example, if we have the exponential function y = 2^x, the inverse logarithmic function would be x = log base 2 of y. In this case, if we substitute the value of y back into the inverse logarithmic function, we will get the original value of x.
This inverse relationship between exponential and logarithmic functions can be represented mathematically as:
log base a (a^x) = x
and
a^(log base a (x)) = x
Learn more about Exponential and logarithmic functions