Question
What is the first step in establishing that log(107⋅5)=7+log5
?(1 point)
Responses
The first step is to rewrite the expression using multiplication, such that log(107⋅5)=log107⋅log5
.
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)
.
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 make 5 an exponent, such that log(107⋅5)=log(107⋅5)
.
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 addition, such that log(107⋅5)=log107+log5
.
?(1 point)
Responses
The first step is to rewrite the expression using multiplication, such that log(107⋅5)=log107⋅log5
.
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)
.
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 make 5 an exponent, such that log(107⋅5)=log(107⋅5)
.
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 addition, such that log(107⋅5)=log107+log5
.
Answers
GPT-4o mini
To establish that \( \log(10^7 \cdot 5) = 7 + \log 5 \), the first step involves understanding how to manipulate the logarithm of a product. The correct response is:
**The first step is to rewrite the expression using addition, such that \(\log(10^7 \cdot 5) = \log(10^7) + \log(5)\).**
This step utilizes the property of logarithms that states \(\log(a \cdot b) = \log(a) + \log(b)\). After this, you can simplify \(\log(10^7)\) to \(7\) (because of another logarithmic property) and thus reach the desired equivalence.
**The first step is to rewrite the expression using addition, such that \(\log(10^7 \cdot 5) = \log(10^7) + \log(5)\).**
This step utilizes the property of logarithms that states \(\log(a \cdot b) = \log(a) + \log(b)\). After this, you can simplify \(\log(10^7)\) to \(7\) (because of another logarithmic property) and thus reach the desired equivalence.