Chapter 7.3, Problem 72PPE

To determine

To solve: The equation $2^x=\frac{1}{32}$ and use the fact if $a^x=a^y$ , then $x=y$ .

Answer to Problem 72PPE

The required answer is $x=-5$ .

Explanation of Solution

Given information:

The given equation $2^x=\frac{1}{32}$ .

Calculation:

  $\begin{array}{l}\Rightarrow 2^x=\frac{1}{32}\\ \Rightarrow 2^x=\frac{1}{2^5}\\ \Rightarrow 2^x=2^{-5}\end{array}$

(Using the fact $a^x=a^y$ )

  $\Rightarrow x=-5$

(Using $x=y$ )