I'm assuming that the exponents are 5x-1 and 3(x+11) even though there are nor parentheses around this expressions.
If that is the case then you would take the common logarithm of both sides:
log(4^5x-1) = log(2^3(x+11))
Then you could use the power rule for logs to get:
(5x-1)(log4) = (3(x+11))(log2)
simplify, and get variable terms on the same side:
(5x-1)/(3x+33) = (log2)/(log4)
use FOIL to multiply the left side, and a calculator to find the value of the right side:
15x^2+162x-33 = .5
subtract .5 from both sides:
15x^2+162x-32.5 = 0
use the quadratic formula to solve for x:
x = -131.34 or -192.66
where'd this problem come from???