Question

Match each function with its corresponding logarithmic inverse function. The exponential functions are f(x)=5^x, f(x)=7^x, f(x)=e^x, f(x)=10^x. The corresponding logarithmic inverse functions are f^-1(x)=log(x), f^-1(x)=log7(x), f^-1(x)=log5(x), f^-1(x)=In(x).

Answer 1

Recall the inverse of a^x is log base a of x. Using ln for natural log and log for base 10:

- f(x) = 5^x → f⁻¹(x) = log₅(x)
- f(x) = 7^x → f⁻¹(x) = log₇(x)
- f(x) = e^x → f⁻¹(x) = ln(x) (the entry labelled "In(x)")
- f(x) = 10^x → f⁻¹(x) = log(x) (common log, base 10)