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Chapter 10: Q. 241 (page 1044)

In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible.
lne416

Short Answer

Expert verified

The value of the expression is4-4ln(2)

Step by step solution

01

Step 1. Given and explanation.

We have lne416.

We know the quotient property of logarithms.
It states that if there is an expression as logamn, it is equal to logam-logan.

The product rule says that if there is an expression asln(xn), it is equal tonln(x).

Applying this property, we will simplify the expression.

02

Step 2. Simplifying the expression. 

We have lne416.

Applying the quotient property, we get
lne4-ln16.

This can be written as lne4-ln(2)4.

Applying the product rule, we get

=4ln(e)-4ln(2)=4-4ln(2)
This gives us the value as4-4ln(2).

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