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

Mar 11, 2016

2

Explanation:

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

$\log \left(2 x \left(x - 1\right)\right) = 2$
Inversely,
$2 x \left(x - 1\right) = {2}^{2}$
${x}^{2} - x - 2 = \left(x + 1\right) \left(x - 2\right) = 0$

The roots are $- 1 \mathmr{and} 2$.
x > 1. The only real solution is x = 2.