# How do you simplify log_2 5 + log_2 x - log_2 10?

${\log}_{2} x - 1$
${\log}_{2} 5 + {\log}_{2} x - {\log}_{2} 10 = {\log}_{2} \left(5 \times \frac{x}{10}\right) = {\log}_{2} \left(\frac{x}{2}\right)$
but ${\log}_{2} \left(\frac{x}{2}\right) = {\log}_{2} x - {\log}_{2} 2 = {\log}_{2} x - 1$