Question

How do you find the inverse of $y = {2^x}$ and is it a function?

Answer 1

Hint:
For solving such a type of question we first interchange the variables, after interchanging the variables we will take logarithm on both of the sides with base two. And after taking logarithm on both of the sides we will solve the equation for y.

Complete step by step solution:
As discussed in hint, in this type of questions in which we have to find the inverse, we have to interchange the variables. So, here we are doing the same,
So, after interchanging the variables we get,
$x = {2^y}$
Now in above equation we will take logarithm on both of the side with base two,
So after taking logarithm on both of the side, equation will became,
${\log _2}x = y{\log _2}2$
now, you already know ${\log _a}a = 1$
so, ${\log _2}x = y(1)$
after rearranging equation we will get our answer,

$y = {\log _2}x$

Note:
As you know now, if you want to solve such a type of question you must have to follow a method. So first try to understand the question and think what is the best and easy way to solve this question. After that find out what has been given to you and use it to find the next step.