$\log_3\left(x+9\right)−\log_3\left(x\right)+\log_5\left(5^2\right)=4$

$\log_3\left(x+9\right)−\log_3\left(x\right)+2=4$

$\log_3\left(x+9\right)−\log_3\left(x\right)=2$

$\log_{3}\left(\frac{x+9}{x}\right)=2$

$3^{2}=\frac{x+9}{x}$

$500\left(1.15\right)^{2x − 1} = 9000$

$\left(1.15\right)^{2x − 1} = 18$

$\log\left(1.15\right)^{2x−1}=\log\left(18\right)$

$\left(2x−1\right)\log\left(1.15\right)=\log\left(18\right)$

$2x-1=\frac{\log(18)}{\log(1.15)}$