`log_4 (x) - log_4 (x - 1) = 1/2` Solve the logarithmic equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 61 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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Note that `log_4(4)=1 `

`log_4x-log_4(x-1)=(1/2)log_4(4) `

Use log rules and condense

`log_(4)(x/(x-1))=log_4(4^(1/2)) `

Exponentiate both sides by 4 and cancel logs:

`x/(x-1)=sqrt4 `

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

`1-1/x=1/2 `

`1/x=1/2 `

`x=2.000 `

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