`ln(x) - ln(x + 1) = 2` Solve the logarithmic equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 55 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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Use the properties of logarithms to condense the ln's

`ln(x/(x+1))=2 `

Rewrite with log

`log_(e)(x/(x+1))=2 `

`(x/(x+1))=e^2 `

`(x+1)/x=1/e^(2) `

`1+1/x=1/e^(2) `

`1/x=1/(e^(2))-1 `

`x=1/((1/e^(2))-1) `


This is a negative number, so it is not in our domain. (logs can only take positive values) There are no real solutions.

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