Answer:
[tex]log_2(\frac{x}{4} )=22[/tex]
which is your answer "D"
Step-by-step explanation:
If [tex]log_4(x)=12[/tex] this means that : [tex]x=4^{12}[/tex] based in the definition of logarithm.
And this exponential expression can also be written using that [tex]4=2^2[/tex]:
[tex]x=4^{12}=(2^2)^{12}=2^{24}[/tex]
so now we know what x is with base 2 (which is needed for the second expression:
[tex]log_2(\frac{x}{4} )=?[/tex]
And this also can be written in exponent form (using the unknown "?" we need to find) as:
[tex]2^?=\frac{x}{4} \\x=4\,*\,2^?\\x=2^2\,*\,2^?\\x=2^{2+?}[/tex]
Since we know the value of x in base 2 (from our first analysis), then:
[tex]x=2^{2+?}=2^{24}\\then\\2+?=24\\?=22[/tex]
Therefore,
[tex]log_2(\frac{x}{4} )=22[/tex]
