Question

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

Answer 1

`q = \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 `\frac{10}{3}` as `(\frac{10}{3})^{-1}` is the same as `0.3`

This means the entire equation is turned into

`(\frac{10}{3})^{-1(2.3q-32)} = (\frac{10}{3})^{q+23}`

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

`-1(2.3q-32)=q+23`

solve for q: `q=\frac{30}{11}`