Question
Evaluate log(1011⋅105)
.(1 point)
.(1 point)
Answers
GPT-4o mini
To evaluate \( \log(1011 \cdot 10^5) \), we can use the property of logarithms that states:
\[
\log(a \cdot b) = \log(a) + \log(b)
\]
Applying this property to our expression:
\[
\log(1011 \cdot 10^5) = \log(1011) + \log(10^5)
\]
Next, we can simplify \( \log(10^5) \):
\[
\log(10^5) = 5 \cdot \log(10) = 5 \cdot 1 = 5
\]
Now our expression becomes:
\[
\log(1011) + 5
\]
Since \(\log(1011)\) does not simplify directly to a known value, we can leave it in its logarithmic form, giving us the final expression:
\[
\log(1011) + 5
\]
Thus, the evaluation of \( \log(1011 \cdot 10^5) \) is:
\[
\log(1011) + 5
\]
\[
\log(a \cdot b) = \log(a) + \log(b)
\]
Applying this property to our expression:
\[
\log(1011 \cdot 10^5) = \log(1011) + \log(10^5)
\]
Next, we can simplify \( \log(10^5) \):
\[
\log(10^5) = 5 \cdot \log(10) = 5 \cdot 1 = 5
\]
Now our expression becomes:
\[
\log(1011) + 5
\]
Since \(\log(1011)\) does not simplify directly to a known value, we can leave it in its logarithmic form, giving us the final expression:
\[
\log(1011) + 5
\]
Thus, the evaluation of \( \log(1011 \cdot 10^5) \) is:
\[
\log(1011) + 5
\]