log₃(x + 9) − log₃x + log₅5² = 4

log₃(x + 9) − log₃x + 2 = 4

log₃(x + 9) − log₃x = 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(1.15)^{2x − 1} = 9000

(1.15)^{2x − 1} = 18

log(1.15)^{2x − 1} = log18

(2x − 1)log(1.15) = 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