Chapter 6 - Exponential Functions and Sequences - 6.5 - Solving Exponential Equations - Monitoring Progress - Page 327: 4

$x=4$

The given equation is $\Rightarrow 4^x=256$ Rewrite $256$ as $4^4$. $\Rightarrow 4^x=4^4$ Equate the exponents. $\Rightarrow x=4$ Check: $(x=4)$ $\Rightarrow 4^4=256$ $\Rightarrow 256=256$ True. Hence, the solution is $x=4$.