SOLUTION: {{{2ln(x^(1/2))-ln(1-x)=2}}}

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: {{{2ln(x^(1/2))-ln(1-x)=2}}}      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 152475: 2ln%28x%5E%281%2F2%29%29-ln%281-x%29=2
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
2%2Aln%28x%5E%281%2F2%29%29-ln%281-x%29+=+2 Apply the power rule to the first term on the left side:a%2Aln%28b%29+=+ln%28b%5Ea%29
ln%28x%29+-+ln%281-x%29+=+2 Now apply the quotient rule to the left side: ln%28a%29-ln%28b%29+=+ln%28a%2Fb%29
ln%28x%2F%281-x%29%29+=+2 Rewrite this in its exponential form: ln%28x%29+=+y---> e%5Ey+=+x
e%5E2+=+x%2F%281-x%29 Multiply both sides by (1-x)
e%5E2%281-x%29+=+x Expand the left side.
e%5E2-e%5E2x+=+x Add e%5E2x to both sides.
e%5E2+=+e%5E2x%2Bx Factor the x on the right side.
e%5E2+=+x%28e%5E2%2B1%29 Divide both sides by %28e%5E2%2B1%29
x+=+e%5E2%2F%28e%5E2%2B1%29 Ths is the exact answer. If you want an approximate answer, then substitute e%5E2+=+7.4 to get:
x+=+7.4%2F8.4
x+=+0.88