Chapter 6 - Exponential Functions and Sequences - 6.5 - Solving Exponential Equations - Exercises - Page 329: 3

$x=2$

The given equation is $\Rightarrow 4^{5x}=4^{10}$ Equate the exponents. $\Rightarrow 5x=10$ Divide each side by $5$ $\Rightarrow \frac{5x}{5}=\frac{10}{5}$ Simplify. $\Rightarrow x=2$ Check: $(x=2)$ $\Rightarrow 4^{5(2)}=4^{10}$ $\Rightarrow 4^{10}=4^{10}$ True. Hence, the solution is $x=2$.