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Natural Logarithm as the Inverse of the Exponential Function

The natural logarithm ln(x) is the inverse of e^x, converting multiplicative factors into additive amounts so that ln(ab) = ln(a) + ln(b) and ln(b^t) = t ln(b). After learning this a student can move between a growth factor and a growth rate, change the base of an exponential expression, and explain why the constant e is singled out as the base whose logarithm is 1.

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Finding the Inverse of Exponential Functions in Precalculus

This concept establishes that the inverse of an exponential function is a logarithmic function, obtained algebraically by swapping the independent and dependent variables in an equation of the form y…