Q. 75 - Precalculus Enhanced with Graphing Utilities

Question

solve each equation. Verify your results using a graphing utility.

$4^x{2}^{x^2}={16}^2$

Step-by-Step Solution

Answer

The value of x for which the above equation is valid are :

$-4,2$

Step 1. Given equation

$4^x{2}^{x^2}={16}^2$

Step 2. Solving exponentially

$$\begin{gathered} 4^x{2}^{x^2}={16}^2 \\ {2}^{2x}.2^{x^2}=2^8 \\ {2}^{x^{2+2x}}=2^8 \\ \Rightarrow x^2+2x=8 \\ {x}^2+2x-8=0 \\ \Rightarrow x=-4,2 \end{gathered}$$