Answer
$q\approx5.662$
Work Step by Step
Divide both sides by $22$ to get $$\frac{10}{22}=0.87^q$$ Next, take the natural log of both sides to get $$\ln \frac{10}{22}=\ln 0.87^q$$ Since $\ln a^b=b \ln a$, this equation simplifies to $$\ln \frac{10}{22}=q \ln 0.87$$ Divide both sides by $\ln 0.87$ to get a solution of $$q=\frac{\ln \frac{10}{22}}{\ln 0.87}\approx5.662$$
