Chapter 6 - Exponential Functions and Sequences - 6.5 - Solving Exponential Equations - Exercises - Page 329: 7

$x=6$

The given equation is $\Rightarrow 2^{x}=64$ Rewrite $64$ as $2^6$ $\Rightarrow 2^{x}=2^6$ Equate the exponents. $\Rightarrow x=6$ Check: $(x=6)$ $\Rightarrow 2^{6}=64$ $\Rightarrow 64=64$ True. Hence, the solution is $x=6$.