Question 630651
{{{log(64, (1/4)) = x}}}
The key here is to notice that both 64 and 1/4 are powers of 4: {{{64 = 4^3}}} and {{{1/4 = 4^((-1))}}}. So this expression will simplify quickly if we change the base to 4.<br>
The change of base formula is
{{{log(a, (p)) = log(b, (p))/log(b, (a))}}}
Using this on our expression, to change the base from 64 to 4, we get:
{{{log(4, (1/4))/log(4, (64)) = x}}}
Since we know what powers of 4 64 and 1/4 are, we can substitute in for those logs:
{{{(-1)/3 = x}}}
And we're finished!