Question

Find the inverse of y=4^x

Answer 1

$y = 4^x \\ \\ \text{The inverse is:}\\\\x = 4^y \Rightarrow 4^y = x\Rightarrow \boxed{y = \log_{4} x}$

Answer 2

Answer:

ln⁡x/ln⁡4  

Step-by-step explanation:

Given

y=4^x

In order to find the inverse of the function the first step is to replace the y with x and x with y

So,

Replacing x with y and y with x

x= 4^y

We have to find the value of y explicitly to find the invers.

The above equation can also be written as:

4^y=x

As the variable is in exponent, to bring it down, ln has to be taken on both sides.

ln⁡ 4^y =ln⁡ x

The power of will be multiplied with the ln.

y ln⁡4=ln⁡x

y=ln⁡x/ln⁡4  

So,

The inverse is ln⁡x/ln⁡4   ..