Question

How do you solve `log_3 x-log_3(x-1)=1`?

Answer 1

`x = 3/2`

Explanation:

`log_3 x-log_3(x-1)=1 = log_3 3` so
`log_3(x/(x-1))=log_3 3` so
`x/(x-1) = 3` or
`x =3(x-1)` Solving for `x` gives

`x = 3/2`. Verifying the feasibility

`log_3 (3/2) - log_3(1/2)=log_3 3`

So, `x = 3/2` is the solution.