`ln(x + 5) = ln(x - 1) - ln(x + 1)` Solve the logarithmic equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 57 - 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 left side of the equation

`ln(x+5)=ln((x-1)/(x+1)) `

Since you have 2 ln's, set the inner parts equal to each other

`x+5=(x-1)/(x+1) `

Simplify,

`x=-3 ` and `x=-2 `

However, since you cannot take the ln or log of a negative number, the answer is

`x=-2 `

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