SOLUTION: solve the following logarithim.... natural log of (x-2)-natural log of (x) = 4

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Question 374141: solve the following logarithim.... natural log of (x-2)-natural log of (x) = 4
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28x-2%29+-+lnx+=+4,
ln%28%28x-2%29%2Fx%29+=+4,
%28x-2%29%2Fx+=+e%5E4, the equivalent exponential equation.
x-2+=+e%5E4%2Ax,after cross-multiplication.
x+-+e%5E4%2Ax+=+2,
x%281-e%5E4%29+=+2,
x+=2%2F+%281-e%5E4%29.
This is approximately equal to -0.0373. Since this value won't satisfy the original equation, we discard this value, and conclude the equation has an empty solution set.