$\log_{3}\left(x + 9\right) − \log_{3}x + \log_{5}5^{2} = 4$

$\log_{3}\left(x + 9\right) − \log_{3}x + 2 = 4$

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

$\text{log}_{3}\frac{x+9}{x}=2$

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

$\frac{x+9}{x}=9$

$x + 9 = 9x$

$9 = 8x$

$x=\frac{9}{8}$

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

$\left(1.15\right)^{2x − 1} = 18$

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

$\left(2x − 1\right)\log\left(1.15\right) = \log18$

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

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

$x ≈ 10.82$