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Algebra Level 1

Given that $\log_4 x= 12,$ then find the value of the below expression.

$\log_2 \left( \dfrac{x}{4} \right)$

-12 48 22 11

2 solutions

Mateus Gomes
Feb 10, 2016

$\log_{2^2}(x)=\frac{1}{2}log_2 (x)=log_2 (x)=(12)(2)$ $\log_2( \dfrac{x}{4})=log_2 (x)-log_2 (4)$ $\log_2( \dfrac{x}{4})=24-2=\Large\color{#3D99F6}{\boxed{22}}$

Erika Fernandez
Oct 13, 2014

With the problem, X=4^12 (x/4)=(4^12)/4=4^11

log(4^11)to the base2 = 11log4to the base 2

=11(2) =22

With the problem, $x = 4^{12} (x/4) = (4^{12})/4=4^{11} log(4^{11})$ to the base $2=11 log 4$ to the base $2$

$=11(2) = 22$

Connor Switala - 6 years, 8 months ago

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