What is "q" equal to in this equation? (0.3)^(2.3q-32)=(10/3)^(q+23)(0.3)2.3q32=(103)q+23

1 Answer
Jun 10, 2018

q = \frac{30}{11}q=3011

Explanation:

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

The 0.30.3 on the LHS can be turned into \frac{10}{3}103 as (\frac{10}{3})^{-1}(103)1 is the same as 0.30.3

This means the entire equation is turned into

(\frac{10}{3})^{-1(2.3q-32)} = (\frac{10}{3})^{q+23}(103)1(2.3q32)=(103)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+231(2.3q32)=q+23

solve for q: q=\frac{30}{11}q=3011