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(-162)+or-sqr rt(162^2-4(15)(-32.5))/(2(15))

x-162+or-sqr rt(28194))/30

or:

x = -131.34 or -192.66

where'd this problem come from???

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