Question:
Evaluate: \( 8^{\log_5 5} \)
Evaluate: \( 8^{\log_5 5} \)
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N/A
Updated On: Apr 23, 2025
- \( \log_5 25 \)
- 120
- 125
- \( \log_5 15 \)
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The Correct Option is C
Solution and Explanation
\[ 8^{\log_5 5} = (2^3)^{\log_5 5} = 2^{3 \cdot \log_5 5} \] \[ = 2^{\log_5 (5^3)} = 2^{\log_5 125} \] Now apply the identity \( a^{\log_b b^k} = k \Rightarrow 2^{\log_5 125} = 125 \)
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