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Chapter 10: Q. 284 (page 1046)

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

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 forloga5xbut it cannot be applicable forloga5+x.

Step by step solution

01

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.

logbMN=logbM+logbNforb>0

02

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

It is applicable for loga5xbut not for loga5+xbecause loga5xis written as product of two exponents butloga5+xis not written as product of two exponents.

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