Question
What is the first step in establishing that log(10
7
⋅5)=7+log5?
A. The first step is to rewrite the expression using multiplication, such that log(10
7
⋅5)=log10
7
⋅log5.
B. The first step is to make 5 an exponent, such that log(10
7
⋅5)=log(10
7⋅5
).
C. The first step is to move the exponent in front of the logarithm, such that log(10
7
⋅5)=7log(10⋅5).
D. The first step is to rewrite the expression using addition, such that log(10
7
⋅5)=log10
7
+log5.
7
⋅5)=7+log5?
A. The first step is to rewrite the expression using multiplication, such that log(10
7
⋅5)=log10
7
⋅log5.
B. The first step is to make 5 an exponent, such that log(10
7
⋅5)=log(10
7⋅5
).
C. The first step is to move the exponent in front of the logarithm, such that log(10
7
⋅5)=7log(10⋅5).
D. The first step is to rewrite the expression using addition, such that log(10
7
⋅5)=log10
7
+log5.
Answers
GPT-4o mini
To establish that \( \log(10^7 \cdot 5) = 7 + \log 5 \), the correct first step involves using the property of logarithms that states \( \log(a \cdot b) = \log a + \log b \).
Therefore, the correct answer is:
**D. The first step is to rewrite the expression using addition, such that \( \log(10^7 \cdot 5) = \log(10^7) + \log(5) \).**
From there, you can apply the property that \( \log(10^7) = 7 \) to get to the final expression.
Therefore, the correct answer is:
**D. The first step is to rewrite the expression using addition, such that \( \log(10^7 \cdot 5) = \log(10^7) + \log(5) \).**
From there, you can apply the property that \( \log(10^7) = 7 \) to get to the final expression.