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Chapter 10: Q. 236 (page 1044)

In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible.

log416y.

Short Answer

Expert verified

The value of the given expression is2-log4y.

Step by step solution

01

Step 1. Given and explanation.

We have log416y.

We know the quotient property of logarithms.

It states that if there is an expression aslogamn, it is equal to logam-logan.

Applying this property, we will simplify the expression.

02

Step 2. Simplifying the expression.

We have log416y.

Applying the quotient property, we get
log416y=log416-log4y=2-log4y
log416is equal to 2because 4raised to the power 2is 16. Thus we get the value as2-log4y.

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