Colon Harrington
06/21/2024 · Middle School
Find the exact value of the logarithm without using a calcula \( \log _{5} 125 \) \( \log _{5} 125=\square \) (Type an integer or a simplified fraction.)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find the value of \( \log_{5} 125 \), we start by expressing 125 as a power of 5.
We know that:
\[
125 = 5^3
\]
Now we can substitute this into the logarithm:
\[
\log_{5} 125 = \log_{5} (5^3)
\]
Using the property of logarithms that states \( \log_{b} (b^x) = x \), we can simplify:
\[
\log_{5} (5^3) = 3
\]
Thus, the exact value of \( \log_{5} 125 \) is:
\[
\boxed{3}
\]
Quick Answer
\( \log_{5} 125 = 3 \)
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