This problem becomes simple if you understand the meaning of logarithms, and recall some simple rules.
Note that by the log conversion formula, Log4x = Log2x/Log24, so the problem becomes
log2x(1 + 1/Log24) = 2, so (1.5)log2x = 2 or log2x = 2/(1.5) = 4/3,
Now remember, log2x = 4/3 means "the power that you raise 2 to in order to get x is 4/3", so x = the cube root of 24.
x = cube root of 16.