Chapter 7.3, Problem 55PPS

To determine

To solve the given equation.

Answer to Problem 55PPS

  $x=\frac{3}{2}$

Explanation of Solution

Given:

Equation:

  $4^{3x}=512$

Calculation:

  $\Rightarrow 4^{3x}=512$

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

  $\Rightarrow 2^{6x}={(2)}^9$

Comparing on both sides,

  $\begin{array}{l}\Rightarrow 6x=9\\ \Rightarrow 2x=3\\ \Rightarrow x=\frac{3}{2}\end{array}$

Conclusion:

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