Question

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

Answer 1

`x = sqrt(11)`

Explanation:

`log a + log b = log (ab)`
`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^2-1 = 10`
`x = +- sqrt(11)`

Since `x > 1`, `x = sqrt(11)`