Question

What is the inverse of a logarithmic function?

Answer 1

The inverse of a logarithmic function is exponential function.

Explanation:

The inverse of a logarithmic function is exponential function:
`color(white)(xxx)f^-1(x)=g^-1(a^x)`
Because logarithmic fuction is
`color(white)(xxx)f(x)=log_a g(x)`
`=>g(x)=a^f(x)`
`=>g^-1(g(x))=g^-1(a^f(x))`
`=>x=g^-1(a^f(x))`
`=>f^-1(x)=g^-1(a^x)`

Considering f(x)=x is axis of symmetry, for `g(x)=x` and `a=10`,