Bush French
02/02/2024 · Middle School
of \( \log _{5} 25 \) is,
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Tutor-Verified Answer
Step-by-step Solution
To find \( \log_{5} 25 \), we can use the property of logarithms that states \( \log_{b} a^n = n \cdot \log_{b} a \).
First, we can express 25 as a power of 5:
\[
25 = 5^2
\]
Now we can substitute this into the logarithm:
\[
\log_{5} 25 = \log_{5} (5^2)
\]
Using the property of logarithms mentioned earlier, we have:
\[
\log_{5} (5^2) = 2 \cdot \log_{5} 5
\]
Since \( \log_{5} 5 = 1 \), we can simplify this further:
\[
2 \cdot \log_{5} 5 = 2 \cdot 1 = 2
\]
Thus, the value of \( \log_{5} 25 \) is
\[
\boxed{2}
\]
Quick Answer
The value of \( \log_{5} 25 \) is 2.
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