Subjects algebra

Logarithm Power 6Cefe5

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Question: Using an appropriate property of logarithms, $3 \cdot \log_5 4$ can be expressed as which single logarithm?
1. **State the problem:** We want to express $3 \cdot \log_5 4$ as a single logarithm. 2. **Recall the logarithm power rule:** The property $a \cdot \log_b c = \log_b (c^a)$ allows us to rewrite the product of a constant and a logarithm as a single logarithm with the argument raised to that constant. 3. **Apply the property:** $$3 \cdot \log_5 4 = \log_5 (4^3)$$ 4. **Calculate the power:** $$4^3 = 4 \times 4 \times 4 = 64$$ 5. **Final expression:** $$3 \cdot \log_5 4 = \log_5 64$$ **Answer:** $\log_5 64$