# What is "q" equal to in this equation? (0.3)^(2.3q-32)=(10/3)^(q+23)

Jun 10, 2018

$q = \setminus \frac{30}{11}$

#### Explanation:

In order to get a linear equation involving q, the bases of the powers on both sides have to equal the same.

The $0.3$ on the LHS can be turned into $\setminus \frac{10}{3}$ as ${\left(\setminus \frac{10}{3}\right)}^{- 1}$ is the same as $0.3$

This means the entire equation is turned into

${\left(\setminus \frac{10}{3}\right)}^{- 1 \left(2.3 q - 32\right)} = {\left(\setminus \frac{10}{3}\right)}^{q + 23}$

This means the powers can equal each other due to same bases so a linear equation such can be formed:

$- 1 \left(2.3 q - 32\right) = q + 23$

solve for q: $q = \setminus \frac{30}{11}$