SOLUTION: I need to simplify the following fraction Numerator - log2(1/4) Denominator log2 16 I get the denominator can be simplified to 4 log2 16, but I can't work out how to match t

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Question 708280: I need to simplify the following fraction
Numerator - log2(1/4)
Denominator log2 16
I get the denominator can be simplified to 4 log2 16, but I can't work out how to match top and bottom how to equalize the logs to leave a simplified answer....any help gratefully appreciated
Found 2 solutions by jsmallt9, josmiceli:
Answer by jsmallt9(3759) (Show Source):
You can put this solution on YOUR website!

Since 1/4 and 16 are both powers of 2, we can figure this out "by hand".

For the numerator, just ask yourself: "What power of 2 is 1/4?" or "2 to what power equals 1/4?" The answer to these equations will be your numerator. Hint:

For the denominator, just ask yourself: "What power of 2 is 16?" or "2 to what power equals 16?" The answer to these equations will be your denominator. This should not be hard to figure out if you just try different powers of 2.

Your final, fully simplified answer should be:

P.S. This may be just a coincidence by your original expression is what you get if you apply the change of base formula:

to change

into base 2 logarithms.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!

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Now I have