SOLUTION: what is the solution to the equation log4 of 4x + 2log4 of x = 4a

Question 670878: what is the solution to the equation log4 of 4x + 2log4 of x = 4a

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the answer is x = 4
here's how.
your equation is:
log4(4x) + 2log4(x) = 4
since a*log(b) = log(b^a), this equation becomes:
log4(4x) + log4(x^2) = 4
since log(a) + log(b) = log(a*b), this equation becomes:
log4(4x * x^2) = 4
simplify this to get:
log4(4x^3) = 4
since logb(x) = y if and only if b^y = x, this equation becomes:
4^4 = 4x^3
since 4^4 = 256, this equation becomes:
256 = 4x^3
divide both sides of this equation by 4 to get:
64 = x^3
take the third root of both sides of this equation to get:
x = 4

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