Pearson George
01/15/2024 · Senior High School
Find the logarithm without using your calculator. \( \log _{10}(100000)=\square \) Preview
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Tutor-Verified Answer
Step-by-step Solution
To find \( \log_{10}(100000) \), we can express \( 100000 \) in terms of powers of \( 10 \).
We know that:
\[
100000 = 10^5
\]
Now, we can use the property of logarithms that states:
\[
\log_b(a^c) = c \cdot \log_b(a)
\]
Applying this property, we have:
\[
\log_{10}(100000) = \log_{10}(10^5) = 5 \cdot \log_{10}(10)
\]
Since \( \log_{10}(10) = 1 \), we can simplify further:
\[
\log_{10}(100000) = 5 \cdot 1 = 5
\]
Thus, the value of \( \log_{10}(100000) \) is:
\[
\boxed{5}
\]
Quick Answer
\( \log_{10}(100000) = 5 \)
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