# How do you solve log_6x-log_6(x+6)=1?

Jul 11, 2016

$x = - 7.2$

#### Explanation:

Use rules of logs on left hand side:

${\log}_{6} \left(\frac{x}{x + 6}\right) = 1$

$\frac{x}{x + 6} = 6$

$x = 6 x + 36 \implies - 5 x = 36$

$\therefore x = - 7.2$

If you sub that into your calculator to check you'll get an error - this is because we need a complex valued logarithm to deal with this! It isn't necessary to solve the question but you might be interested enough to look it up