Question
Evaluate log(1011⋅105)
.(1 point)
.(1 point)
Answers
GPT-4o mini
To evaluate \( \log(1011 \cdot 10^5) \), we can use the properties of logarithms, specifically the product property, which states that \( \log(a \cdot b) = \log(a) + \log(b) \).
Applying this property:
\[
\log(1011 \cdot 10^5) = \log(1011) + \log(10^5)
\]
Next, we can evaluate \( \log(10^5) \). Using the power property of logarithms:
\[
\log(10^5) = 5 \cdot \log(10) = 5
\]
Now, we just need to add \( \log(1011) \) to this result:
\[
\log(1011 \cdot 10^5) = \log(1011) + 5
\]
Thus, the final expression is:
\[
\log(1011 \cdot 10^5) = \log(1011) + 5
\]
Without further calculators or tables to evaluate \( \log(1011) \), we can only express the result as \( \log(1011) + 5 \). However, if an approximation is needed, \( \log(1011) \) is approximately \( 3.004321 \), leading to an estimate:
\[
\log(1011 \cdot 10^5) \approx 3.004321 + 5 \approx 8.004321
\]
The exact answer is:
\[
\log(1011) + 5
\]
Applying this property:
\[
\log(1011 \cdot 10^5) = \log(1011) + \log(10^5)
\]
Next, we can evaluate \( \log(10^5) \). Using the power property of logarithms:
\[
\log(10^5) = 5 \cdot \log(10) = 5
\]
Now, we just need to add \( \log(1011) \) to this result:
\[
\log(1011 \cdot 10^5) = \log(1011) + 5
\]
Thus, the final expression is:
\[
\log(1011 \cdot 10^5) = \log(1011) + 5
\]
Without further calculators or tables to evaluate \( \log(1011) \), we can only express the result as \( \log(1011) + 5 \). However, if an approximation is needed, \( \log(1011) \) is approximately \( 3.004321 \), leading to an estimate:
\[
\log(1011 \cdot 10^5) \approx 3.004321 + 5 \approx 8.004321
\]
The exact answer is:
\[
\log(1011) + 5
\]