Subjects algebra

Logarithm Sum E3F93B

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Simplify the expression $\log_9 3 + \log_9 27$. 2. **Recall the logarithm property:** The sum of logarithms with the same base is the logarithm of the product: $$\log_b x + \log_b y = \log_b (xy)$$ 3. **Apply the property:** $$\log_9 3 + \log_9 27 = \log_9 (3 \times 27)$$ 4. **Calculate the product:** $$3 \times 27 = 81$$ 5. **Rewrite the expression:** $$\log_9 81$$ 6. **Express 81 as a power of 9:** Since $9^2 = 81$, we have $$\log_9 9^2$$ 7. **Use the logarithm power rule:** $$\log_b b^k = k$$ 8. **Evaluate:** $$\log_9 9^2 = 2$$ **Final answer:** $$\boxed{2}$$