Chapter 6 - Exponential Functions and Sequences - 6.5 - Solving Exponential Equations - Monitoring Progress - Page 326: 1

$x=3$

The given equation is $\Rightarrow 2^{2x}=2^6$ Equate the exponents. $\Rightarrow 2x=6$ Divide each side by $2$. $\Rightarrow \frac{2x}{2}=\frac{6}{2}$ Simplify. $\Rightarrow x=3$ Check $x=3$. $\Rightarrow 2^{2x}=2^6$ $\Rightarrow 2^{2(3)}=2^6$ $\Rightarrow 2^{6}=2^6$ True.