SOLUTION: Please show me how to work this problem i know the answer is (4e^(2/3))/3e {{{ln4x-ln3-2lnx=(1/3)}}}

Question 64571: Please show me how to work this problem i know the answer is (4e^(2/3))/3e

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!

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Question 64576 in Exponential-and-logarithmic-functions:
the answer is the answer is (4e^(2/3))/3e but i need work please help
ln4x-ln3-2lnx=(1/3)

the answer is the answer is (4e^(2/3))/3e but i need work please help
ln4x-ln3-2lnx=(1/3)
USE FORMULAE
LN(X/Y)=LN(X)-LN(Y)
LN(X)+LN(Y)=LN(XY)
A*LN(X)=LN(X^A)
AND IF
LN(X)=A
X=E^A
LN(4X)-LN(3)-2LN(X)= LN(4X/3)-LN(X^2)=LN[4X/3X^2)=LN[4/(3X)]=1/3
E^(1/3)=4/(3X)
X=(4/3)[E^(-1/3)]=4/{3*E^(1/3)}=[4E^(2/3)]/[3*{E^(1/3)}{E^(2/3)}]
=[4*E^(2/3)/(3E)]
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