Question

What is inverse of f(x)=4^x ?

Answer 1

`\huge\boxed{f^(-1)(x)=\log_4x,\ \text{for}\ x\in\mathbb{R^+}}`

Explanation:

`f(x)=4^x\to y=4^x\\\\\text{Domain:}x\in\mathbb{R}\\\\\text{Exchange}\ x\ \text{to}\ y\ \text{and vice versa}:\\\\x=4^y\\\\\text{Solve for}\ y:\\\\4^y=x\Rightarrow\log_44^y=\log_4x\qquad\text{use}\ log_ab^n=n\log_ab\\\\y\log_44=\log_4x\qquad\text{use}\ \log_aa=1\\\\y=\log_4x\\\\\text{Domain:}\ x\in\mathbb{R^+}`