Question

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

Answer 1

`x = 11/9`

Explanation:

`log a - log b = log(a/b)`
`log_a b = c <=> a^c = b`

`log (x+1) - log (x-1) = 1`
`log (x+1)/(x-1) = 1`
Assuming `log` base 10:
`(x+1)/(x-1) = 10`
`x+1 = 10(x-1)`
`x = 11/9`