Chapter 7.3, Problem 49PPS

To determine

To solve the given equation.

Answer to Problem 49PPS

  $x=\frac{3}{2}$

Explanation of Solution

Given:

Equation:

  $9^x=27$

Formula used:

  ${\left(a^n\right)}^m=a^{nm}$

Calculation:

  $\Rightarrow 9^x=27$

  $\Rightarrow {(3\times 3)}^x=(3\times 3\times 3)$

  $\Rightarrow {(3^2)}^x={(3)}^3$

  $\Rightarrow 3^{2x}=3^3$

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

Comparing on both sides,

  $\begin{array}{l}\Rightarrow 2x=3\\ \Rightarrow x=\frac{3}{2}\end{array}$

Conclusion:

Therefore, the required solution for the given equation is $x=\frac{3}{2}$ .