`ln(root(3)(x/y))` 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 51 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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

Given,

`ln(root(3)(x/y)) `

Then,

`ln(root(3)(x/y))=ln(root(3)x)-ln(root(3)y)`

Therefore, after bringing the exponent down,

`ln(root(3)(x/y)) = (1/3)lnx-(1/3)lny`

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