Question 708280
{{{log(2, (1/4))/log(2, (16))}}}
Since 1/4 and 16 are both powers of 2, we can figure this out "by hand".<br>
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: {{{2^(-1) = 1/2}}}<br>
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.<br>
Your final, fully simplified answer should be:
{{{-1/2}}}<br>
P.S. This may be just a coincidence by your original expression is what you get if you apply the change of base formula:
{{{log(a, (p)) = log(b, (p))/log(b, (a))}}}
to change
{{{log(16, (1/4))}}}
into base 2 logarithms.