Question 689697
{{{log(64, (1/4))=x}}}
The expression on the left represents the exponent for 64 that results in 1/4. If you are really sharp with your exponents you will already know what this exponent is. If not then we can use the change of base formula, {{{log(a, (p)) = log(b, (p))/log(b, (a))}}}, to convert the base 64 log into a log with a different base. This different base should be one that will make it easy to figure out the value of the log. With an argument of 1/4 a base of 4 looks good. Using the change of base formula to change to base 4 logs we get:
{{{log(4, (1/4))/log(4, (64))=x}}}
After checking various powers of 4 you should know what these two logs are. The power of 4 that equals 1/4 is -1 and the power of 4 that equals 64 is 3. So our expression simplifies to:
{{{(-1)/3}}}<br>
P.S. Look back at the original expression. See if you can understand why
{{{log(64, (1/4))=-1/3}}}