`log_2 (sqrt(a - 1)/9), a > 1` Use the properties of logarithms to expand the expression as a sum, difference, and or constant multiple of logarithms. (Assume all variables are positive.)

Textbook Question

Chapter 3, 3.3 - Problem 49 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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Expand using subtraction because the terms inside the log are being divided.

Given,

`log_2(sqrt(a-1)/9) `

Then,

`log_2(sqrt(a-1)/9)=log_2(a-1)^(1/2)-log_2(9) `

Therefore, after bring down the exponents, this simplifies to,

`log_2(sqrt(a-1)/9)=(1/2)log_2(a-1)-log_2(9)`

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