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Chapter 12: Problem 101

You overhear a student talking about a property of logarithms in which division becomes subtraction. Explain what the student means by this.

Short Answer

Expert verified
The property of logarithms where division becomes subtraction is known as the logarithm of a quotient rule. Mathematically, it's expressed as \( \log_a \frac{m}{n} = \log_a m - \log_a n \). It means that the logarithm of a quotient (division) is equal to the difference (subtraction) of the logarithms.

Step by step solution

01

Understand the Logarithm of a Quotient Rule

This property is also known as the logarithm of a quotient rule. The rule states that the logarithm of a quotient is equal to the difference of the logarithms. In mathematical terms, if a and b are positive numbers then the rule can be written as \( \log_a \frac{m}{n} = \log_a m - \log_a n \)
02

Example

To illustrate what it means, suppose you have \( \log \frac{100}{10} \). According to the logarithm of a quotient rule, this can be written as \( \log 100 - \log 10 \). So, this property essentially transforms the division operation into a subtraction operation in the context of logarithms.

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