SOLUTION: Express y in terms of x when: ln y - ln(y+1) = ln x

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Question 998138: Express y in terms of x when:
ln y - ln(y+1) = ln x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28y%29-ln%28y%2B1%29=ln%28x%29 Start with the given equation


ln%28y%2F%28y%2B1%29%29=ln%28x%29 Use rule 2


y%2F%28y%2B1%29=x See note below


y=x%28y%2B1%29 Multiply both sides by y+1.


y=xy%2Bx Distribute


y-xy=x Subtract xy from both sides.


y%281-x%29=x Factor


y=x%2F%281-x%29 Divide both sides by 1-x.


Note: if log%28%28x%29%29=log%28%28y%29%29, then x=y. This is true for any log of any base.