The Product Rule of Logarithms Quick Check
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Question
What is the first step in establishing that log(107⋅5)=7+log5
?(1 point)
Responses
The first step is to move the exponent in front of the logarithm, such that log(107⋅5)=7log(10⋅5)
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The first step is to move the exponent in front of the logarithm, such that logarithm left parenthesis 10 superscript 7 baseline times 5 right parenthesis equals 7 logarithm left parenthesis 10 times 5 right parenthesis .
The first step is to rewrite the expression using addition, such that log(107⋅5)=log107+log5
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The first step is to rewrite the expression using addition, such that logarithm left parenthesis 10 superscript 7 baseline times 5 right parenthesis equals logarithm 10 superscript 7 baseline plus logarithm 5 .
The first step is to make 5 an exponent, such that log(107⋅5)=log(107⋅5)
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The first step is to make 5 an exponent, such that logarithm left parenthesis 10 superscript 7 baseline times 5 right parenthesis equals logarithm left parenthesis 10 superscript 7 times 5 baseline right parenthesis .
The first step is to rewrite the expression using multiplication, such that log(107⋅5)=log107⋅log5
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The first step is to rewrite the expression using multiplication, such that logarithm left parenthesis 10 superscript 7 baseline times 5 right parenthesis equals logarithm 10 superscript 7 baseline times logarithm 5 .
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1 answer
To establish that \( \log(10^7 \cdot 5) = 7 + \log 5 \), the correct first step involves using the property of logarithms related to multiplication. Specifically, the product rule states that \( \log(a \cdot b) = \log a + \log b \).
Thus, the correct response is:
The first step is to rewrite the expression using addition, such that \( \log(10^7 \cdot 5) = \log 10^7 + \log 5 \).
