# How do you solve log3(x+1) - log5(x-2)=2?

May 6, 2016

$x = \frac{497}{1003}$

#### Explanation:

$\log 3 \left(x + 1\right) - \log 5 \left(x - 2\right) = 2$

or $\log \frac{3 \left(x + 1\right)}{5 \left(x - 2\right)} = \log 100$

or $\frac{3 \left(x + 1\right)}{5 \left(x - 2\right)} = 100$

or $3 x + 3 = 100 \times \left(5 x - 10\right)$

or $3 x + 3 = 500 x - 1000$

or $497 x = 1003$

or $x = \frac{497}{1003}$