Chapter 6.3, Problem 45E

To determine

To calculate: The inverse of the function.

Answer to Problem 45E

The inverse of the function $y={\log }_{2}x$ is $2^y=x$ .

Explanation of Solution

Given information:

The given function is $y={\log }_{2}x$ .

Formula Used:

Logarithmic power rule is

If ${\log }_{a}b$ is a logarithmic function then the exponential form $a^{{\log }_{a}b}$ is equal to $b$ .

Calculation:

Consider the logarithmic function is $y={\log }_{2}x$ .

Convert the logarithmic form into exponential form.

Take exponential in each side with base 2. Use the power rule.

  $\begin{array}{c}y={\log }_{2}x\\ 2^y=2^{{\log }_{2}x}\\ 2^y=x\end{array}$

Hence, the inverse of the function $y={\log }_{2}x$ is $2^y=x$ .