Coleman Morgan
01/23/2024 · Elementary School
Evaluate. \[ \log _{3} 81 \]
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Tutor-Verified Answer
Step-by-step Solution
To evaluate \( \log_{3} 81 \), we start by expressing 81 as a power of 3.
We know that:
\[
81 = 3^4
\]
Now we can substitute this into the logarithm:
\[
\log_{3} 81 = \log_{3} (3^4)
\]
Using the property of logarithms that states \( \log_{b} (a^n) = n \cdot \log_{b} a \), we can simplify:
\[
\log_{3} (3^4) = 4 \cdot \log_{3} 3
\]
Since \( \log_{3} 3 = 1 \), we have:
\[
4 \cdot \log_{3} 3 = 4 \cdot 1 = 4
\]
Thus, the value of \( \log_{3} 81 \) is:
\[
\boxed{4}
\]
Quick Answer
The value of \( \log_{3} 81 \) is 4.
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