Chapter 10: Q. 284 (page 1046)

Write the Product Property in your own words. Does it apply to each of the following? $\log_{a} 5 x, \log_{a} (5 + x)$ .Why or why not?

Short Answer

Expert verified

The product property for logarithms can be used to simplify a logarithm of a product by rewriting it as a sum of individual logarithms.

It can be applicable for $\log_{a} 5 x$ but it cannot be applicable for $\log_{a} (5 + x)$ .

Step by step solution

Step 1. Define product property of logarithm

The product property for logarithms can be used to simplify a logarithm of a product by rewriting it as a sum of individual logarithms.

$\log_{b} M N = \log_{b} M + \log_{b} N f o r b > 0$

Step 2. Tell for which of the given expression product property is applicable with reason

It is applicable for $\log_{a} 5 x$ but not for $\log_{a} (5 + x)$ because $\log_{a} 5 x$ is written as product of two exponents but $\log_{a} (5 + x)$ is not written as product of two exponents.

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Write the Product Property in your own words. Does it apply to each of the following? $\log_{a} 5 x, \log_{a} (5 + x)$ .Why or why not?

Short Answer

Step by step solution

Step 1. Define product property of logarithm

Step 2. Tell for which of the given expression product property is applicable with reason

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Write the Product Property in your own words. Does it apply to each of the following? loga5x,loga5+x.Why or why not?

Short Answer

Step by step solution

Step 1. Define product property of logarithm

Step 2. Tell for which of the given expression product property is applicable with reason

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Decision Maths

Calculus

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Write the Product Property in your own words. Does it apply to each of the following? $\log_{a} 5 x, \log_{a} (5 + x)$ .Why or why not?