Question

Sorry got a lot today lol 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 rewrite the expression using addition, such that log(107⋅5)=log107+log5 . 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) . 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 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 .

Answer 1

To establish that \( \log(10^7 \cdot 5) = 7 + \log 5 \), the first correct step is to rewrite the expression using addition, which follows from the logarithmic property that states \( \log(a \cdot b) = \log a + \log b \).

Therefore, the appropriate choice is:

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

This allows you to apply the property of logarithms to separate the terms, leading to the next step where you can then rewrite \( \log 10^7 \) as \( 7 \).

Answer 2

Hey you didnt laugh at my joke