What is the first step in establishing that log(107⋅5)=7+log5

Question

?(1 point)
Responses

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 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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Answer 1

The correct first step in establishing that \( \log(10^7 \cdot 5) = 7 + \log 5 \) is:

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

This uses the property of logarithms that states \( \log(a \cdot b) = \log(a) + \log(b) \). From there, you can then move the exponent in front of the logarithm, yielding \( \log(10^7) = 7 \). Therefore, it leads to the final expression.