# How do you solve log_5(x - 1) + log_5(x - 2) - log_5(x + 6) = 0?

Jun 22, 2018

color(crimson)(x = +- 2sqrt2

#### Explanation:

${\log}_{5} \left(x - 1\right) + {\log}_{5} \left(x - 2\right) - {\log}_{5} \left(x + 6\right) = 0$

color(blue)(log a + log b = log (ab), log x - log y = log(x/y), " as per log rules"

${\log}_{5} \left(\frac{\left(x + 1\right) \left(x - 2\right)}{x + 6}\right) = 0$

$\frac{\left(x + 1\right) \left(x - 2\right)}{x + 6} = {5}^{0} = 1$

$\left(x + 1\right) \left(x - 2\right) = x + 6$

${x}^{2} - x - 2 = x + 6$

color(crimson)(x^2 = 8 " or " x = +- 2 sqrt2