SOLUTION: (3x)^(log3)-(5x)^(log5)=0 Solve for x

Question 391533: (3x)^(log3)-(5x)^(log5)=0
Solve for x
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
(3x)^(log3)-(5x)^(log5)=0
Solve for x
(log3)(log3x)-(log5)(log5x)=0
log3(log3+logx)-log5(log5+logx)=0
(log3)^2+(log3)(logx)-(log5)^2-(log5)(logx)=0
(log3)(logx)-(log5)(logx)=(log5)^2-(log3)^2 (difference of 2 squares)
logx(log3-log5)=(log5-log3)(log5+log3)
logx=(log5-log3)(log5+log3)/-(log5-log3)
logx=-(log5+log3)=-1.17609
x=10^-1.17609=.06667 (definition of a logarithm, the base raised to the logarithm of the number is equal to the number)
ans: x=.06667
Check: (3*.06667)^log3-(5*.06667)^log5 = 0
= .464-.464 = 0

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