LOGging Problem

Algebra Level 2

If Log 4 (x) = 12, then log 2 (x / 4) is equal to

11 22 70 -12

1 solution

Omkar Kulkarni
Feb 2, 2015

$\log_{4}{x}=12$

$\frac{\log_{}{x}}{\log_{}{4}}=12$

$\frac{\log_{}{x}}{\log_{}{2^{2}}}=12$

$\frac{\log_{}{x}}{2\log_{}{2}}=12$

$\frac{\log_{}{x}}{\log_{}{2}}=12$

$\log_{2}{x}=24$

$\therefore \log_{2}{\frac{x}{4}} = \log_{2}{x} - \log_{2}{4} = 24 - 2 = \boxed{22}$