Question

How do you solve `log_2 2x + log_2(x-1)=2`?

Answer 1

2

Explanation:

log here is a binary (base 2) log.
log a + log b = log ab.

`log (2x(x-1)) = 2`
Inversely,
`2x(x-1) = 2^2`
`x^2-x-2 = (x+1)(x-2)=0`

The roots are `-1 and 2`.
x > 1. The only real solution is x = 2.