Subjects algebra

Logarithm Evaluation 13C692

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1. **State the problem:** Evaluate the expression $\log_3 27 - \log_2 4$. 2. **Recall the logarithm rules:** - $\log_b a$ means the power to which the base $b$ must be raised to get $a$. - The subtraction of logarithms with different bases cannot be combined directly. 3. **Evaluate each logarithm separately:** - $\log_3 27$: Since $27 = 3^3$, we have $\log_3 27 = 3$. - $\log_2 4$: Since $4 = 2^2$, we have $\log_2 4 = 2$. 4. **Substitute the values back into the expression:** $$\log_3 27 - \log_2 4 = 3 - 2$$ 5. **Calculate the final answer:** $$3 - 2 = 1$$ **Final answer:** $1$