Question 20202
You can solve for x by taking the logarithm of both sides of the equation and solving for x.

{{{log(64^x) = log(4)}}}
{{{xlog64 = log(4)}}} Divide both sides by log64
{{{x = log4/log64}}}
{{{x = log4/log4^3}}}
{{{x = log4/3log4}}}
{{{x = 1/3}}}

Check:

{{{64^(1/3) = 4}}}