What Is the Inverse of an Exponential Function?

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The inverse of an exponential function is a logarithm function. An exponential function written as f(x) = 4^x is read as “four to the x power.” Its inverse logarithm function is written as f^-1(y) = log4y and read as “logarithm y to the base four.”

While an exponential function denotes multiplying a number to a certain exponential power, a logarithm function denotes the exponent to which a base must be raised to produce a number. For example, because five to the third power is equal to 125, the log of three to the base of five is equal to 125.