Chapter 11 - Cumulative Review - Page 670: 25c

$x=6$

Expressing both sides of the equal sign with the same base so that the exponents can be equated, then, \begin{array}{l} 4^{x+3}=8^x \\ (2^2)^{x+3}=(2^3)^x \\ 2^{2x+6}=2^{3x} \\ 2x+6=3x \\ 2x-3x=-6 \\ -x=-6 \\ x=6 .\end{array}