# How do you solve 2^x * 4^(x+5)=4^(2x-1)?

Sep 30, 2015

x=12

#### Explanation:

Rewrite the equation with all the exponents with the same base, which would obviously 2.

${2}^{x} \cdot {\left({2}^{2}\right)}^{x + 5} = {\left({2}^{2}\right)}^{2 x - 1}$

${2}^{x} \cdot {2}^{2 x + 10} = {2}^{4 x - 2}$

${2}^{3 x + 10} = {2}^{4 x - 2}$

Since base is same on both sides, equate the exponents 3x+10=4x-2 and solve for x.

x=12