Chapter 7.3, Problem 56PPS

To determine

To solve the given equation.

Answer to Problem 56PPS

  $x=\frac{1}{7}$

Explanation of Solution

Given:

Equation:

  ${128}^{3x}=8$

Calculation:

  $\Rightarrow {128}^{3x}=8$

  $\Rightarrow {(2\times 2\times 2\times 2\times 2\times 2\times 2)}^{x-4}=(2\times 2\times 2)$

  $\Rightarrow {(2^7)}^{3x}={(2)}^3$

  $\Rightarrow 2^{21x}={(2)}^3$

Comparing on both sides,

  $\begin{array}{l}\Rightarrow 21x=3\\ \Rightarrow 7x=1\\ \Rightarrow x=\frac{1}{7}\end{array}$

Conclusion:

Therefore, the required solution for the given equation is $x=\frac{1}{7}$ .