# How do you solve log x - log (9x+4)= -1?

Feb 27, 2016

Use the rule ${\log}_{a} n - {\log}_{a} m = {\log}_{a} \left(\frac{n}{m}\right)$ to simplify

#### Explanation:

$\log \left(\frac{x}{9 x + 4}\right) = - 1$

Convert to exponential form. The log is in base 10, since nothing is noted in subscript beside the log.

$\frac{x}{9 x + 4} = {10}^{-} 1$

$\frac{x}{9 x + 4} = \frac{1}{10} ^ 1$

$\frac{x}{9 x + 4} = \frac{1}{10}$

Simplify using the rule $\frac{a}{b} = \frac{m}{n} \to a \times n = b \times m$

$x \left(10\right) = \left(9 x + 4\right) 1$

$10 x = 9 x + 4$

$10 x - 9 x = 4$

$x = 4$