Chapter 7.3, Problem 50PPS

To determine

To solve the given equation.

Answer to Problem 50PPS

  $x=\frac{2}{5}$

Explanation of Solution

Given:

Equation:

  ${32}^x=4$

Formula used:

  ${\left(a^n\right)}^m=a^{nm}$

Calculation:

  $\Rightarrow {32}^x=4$

  $\Rightarrow {(2\times 2\times 2\times 2\times 2)}^x=(2\times 2)$

  $\Rightarrow {(2^5)}^x={(2)}^2$

  $\Rightarrow 2^{5x}=2^2$

  $[\because {\left(a^n\right)}^m=a^{nm}]$

Comparing on both sides,

  $\begin{array}{l}\Rightarrow 5x=2\\ \Rightarrow x=\frac{2}{5}\end{array}$

Conclusion:

Therefore, the required solution for the given equation is $x=\frac{2}{5}$ .