Question

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

Answer 1

Since the logs are in the same base already, we can use the rule `log_ab - log_ac = log_a(b / c)`

Explanation:

`log(x + 1) - log(x - 1) = 1`

`log((x + 1)/(x - 1)) = 1`

Since this is a base 10, we can now convert to exponential form.

`((x + 1)/(x - 1)) = 10^1`

`x + 1 = 10(x - 1)`

`x + 1 = 10x - 10`

`1 + 10 = 10x - x`

`11 = 9x`

`11/9 = x`

Hopefully you understand now!