# What is the value of x if 2^3(3^(2x + 3)) = 6(2)^2?

Dec 21, 2016

$x = - 1$

#### Explanation:

Isolate the exponent.

${3}^{2 x + 3} = \frac{24}{8}$

${3}^{2 x + 3} = 3$

We are in common bases--logarithms are not necessary.

$2 x + 3 = 1$

$2 x = - 2$

$x = - 1$

Check back in the original equation:

8(3^(2(-1) + 3)) =^? 24

8(3^1) = 24" "color(green)(√)

Practice Exercises

1. Solve each equation by writing in equivalent bases and using laws of exponents.

a) ${3}^{2 x + 5} = {9}^{x - 2}$

b) ${2}^{5 x + 1} / {16}^{3 x} = {8}^{4 x + 2}$

Hopefully this helps!