`log_2 (x) + log_2 (x + 2) = log_2 (x + 6)` Solve the logarithmic equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 60 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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Since they are both `log_2 ` , rewrite it using properties of logs

`log_(2)(x)(x+2)=log_2(x+6) `

Exponentiate both sides by 2 and solve for x

`2^(log_(2)(x)(x+2))= 2^(log_2(x+6))`

`x(x+2)=x+6 `

`x^2+x-6=0 `

`(x+3)(x-2)=0 `

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

Since you cannot take the log of a negative number, `x=-3 ` is not viable.

Therefore, your answer is `x=2 `

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