# How do you solve 32^(1-2X) = 8^(1/3)?

Aug 19, 2015

color(blue)(X=2/5

#### Explanation:

32^(1-2X)=8^(1/3

We know that $32 = {2}^{5}$ and $8 = {2}^{3}$

2^(5(1-2X))=2^(3/3

${2}^{5 \left(1 - 2 X\right)} = {2}^{1}$

Now as bases are equal we equate the powers

$5 \left(1 - 2 X\right) = 1$

$5 - 10 X = 1$

$5 - 1 = 10 X$

$4 = 10 X$
$X = \frac{4}{10}$
color(blue)(X=2/5