Question
Evaluate log (10^2 • 5). Round your answer to the nearest thousandth.
Answers
GPT-4o mini
To evaluate \( \log(10^2 \cdot 5) \), we can first simplify the expression using the properties of logarithms.
1. We can use the product property of logarithms, which states \( \log(a \cdot b) = \log(a) + \log(b) \):
\[
\log(10^2 \cdot 5) = \log(10^2) + \log(5)
\]
2. Now, we can evaluate \( \log(10^2) \):
\[
\log(10^2) = 2
\]
3. Next, we need to find \( \log(5) \). Using a calculator or logarithm table, we find:
\[
\log(5) \approx 0.699
\]
4. Now, we can add the two results together:
\[
\log(10^2 \cdot 5) = 2 + 0.699 = 2.699
\]
5. Finally, rounding to the nearest thousandth, we get:
\[
\log(10^2 \cdot 5) \approx 2.699
\]
Thus, the answer is \( \boxed{2.699} \).
1. We can use the product property of logarithms, which states \( \log(a \cdot b) = \log(a) + \log(b) \):
\[
\log(10^2 \cdot 5) = \log(10^2) + \log(5)
\]
2. Now, we can evaluate \( \log(10^2) \):
\[
\log(10^2) = 2
\]
3. Next, we need to find \( \log(5) \). Using a calculator or logarithm table, we find:
\[
\log(5) \approx 0.699
\]
4. Now, we can add the two results together:
\[
\log(10^2 \cdot 5) = 2 + 0.699 = 2.699
\]
5. Finally, rounding to the nearest thousandth, we get:
\[
\log(10^2 \cdot 5) \approx 2.699
\]
Thus, the answer is \( \boxed{2.699} \).