SOLUTION: What is the solution of the equation 2 log4 (5x) = 3?

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Question 331260: What is the solution of the equation 2 log4 (5x) = 3?
Answer by mathmandotcom(31) About Me  (Show Source):
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Solve 2log4(5x)=3 I assume this reads 2 times log base 4 of 5x equals 3: solve
alog(b)=log(b^a) so 2lod4(5x)=log4((5x)^2)=3 we have log4(25x^2)=3
Using the inverse log rule Log b(a)=c you get a=b^c so
log4(25x^2)=3 25x^2=4^3; 25x^2=64; x^2=64/25; x=sqroot(64/25)=8/5