Question

(log 4 64) / (2 log 4 √4) is equal to

a) log 4 4
b) 4
c) 2 log 4 4
d) 3

Answer 1

well start by writing the values in terms of the bases

\[64 = 4^3\]

\[\sqrt{4} = 4^{\frac{1}{2}}\]

so your question is now

and applying a log law to the numerator to manage the 2

\[\frac{\log_4(64)}{2\log_{4} \sqrt{4}} = \frac{\log_{4}(4^3)}{\log_{4}(4^{\frac{1}{2}})^2}\]

so you are now being asked to simplify

\[\frac{\log_{4}(4^3)}{\log_{4}(4^1)}\]

all you now need to do is know

\[\log_{a}(a^x) = x\]

which says, then the base of the log and base of the exponent are the same tit can be simplified to just the power...

hope it helps

Answer 2

Thank you

Answer 3

So I think it is answer c)

Answer 4

nope... applied the last law I listed

\[\log_{4}(4^3) = 3\]

and

\[\log_{4}(4^1) = 1\]

so you fraction becomes

\[\frac{\log_{4}(4^3)}{\log_{4}(4^1)} = \frac{3}{1} = 3\]

Answer 5

Thank you once again!