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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 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 .

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 .
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Answer 1

To establish that \( \log(10^7 \cdot 5) = 7 + \log 5 \), the first step is to rewrite the expression using the property of logarithms that states \( \log(ab) = \log a + \log b \). This leads us to the equation:

\[ \log(10^7 \cdot 5) = \log(10^7) + \log(5) \]

Here, since \( \log(10^7) = 7 \) (by the definition of logarithms), we can then express it as:

\[ \log(10^7) + \log(5) = 7 + \log(5) \]

Thus, the correct response is:

The first step is to rewrite the expression using addition, such that \( \log(10^7 \cdot 5) = \log(10^7) + \log(5) \).