Question

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

Answer 1

`x=-7.2`

Explanation:

Use rules of logs on left hand side:

`log_6((x)/(x+6)) = 1`

`x/(x+6) = 6`

`x = 6x +36 implies - 5x = 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