SOLUTION: 3logx-2log2x=2log5 could you please show me the steps of completing this question? thanks for your time!

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Question 598827: 3logx-2log2x=2log5
could you please show me the steps of completing this question? thanks for your time!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
3logx-2log2x=2log5
3logx-2log2x-2log5=0
log(x^3)-log(2x)^2-log(5^2)=0
log(x^3)-(log(4x^2)+log(5^2))=0
place under single log
log[(x^3)/(4x^2)*(5^2)]=0
Convert to exponential form: base(10) raised to log of number(0)=number(x-3)/(4x^2)*(5^2)
10^0=(x^3)/(4x^2)*(5^2)=1
(x^3)=(4x^2)*(5^2)=100x^2
x^3-100x^2=0
x^2(x-100)=0
x^2=0
x=0 (reject, x>0)
or
x=100