https://file.aiquickdraw.com/mathbot/file/1727357836388n0vs1tn0.jpg

The question asks for the value of \( \log_3 81 + \log_3 \frac{1}{9} \).

Let's solve it step by step:

1. **Break down the logarithms:**
   - \( \log_3 81 \) is the logarithm of 81 to the base 3.
   - \( \log_3 \frac{1}{9} \) is the logarithm of \( \frac{1}{9} \) to the base 3.

2. **Simplify each term:**
   - \( \log_3 81 \): Since \( 81 = 3^4 \), we have:
     \[
     \log_3 81 = 4
     \]
   - \( \log_3 \frac{1}{9} \): Since \( \frac{1}{9} = 3^{-2} \), we have:
     \[
     \log_3 \frac{1}{9} = -2
     \]

3. **Add the values:**
   \[
   \log_3 81 + \log_3 \frac{1}{9} = 4 + (-2) = 2
   \]

Thus, the correct answer is \( \boxed{2} \), which corresponds to option **c**.

Would you like further details on this solution, or any other explanations?

Here are five related questions for practice:
1. What is \( \log_3 243 \)?
2. Simplify \( \log_3 27 + \log_3 \frac{1}{3} \).
3. Solve \( \log_2 16 + \log_2 \frac{1}{4} \).
4. What is \( \log_5 25 \)?
5. Calculate \( \log_4 64 \).

**Tip:** When working with logarithms, always try to express the number as a power of the base to simplify the calculations.

Nilai dari log3 81 + log3 1/9 adalah ....

Learn how to solve the logarithmic expression log3 81 + log3 1/9 with a detailed step-by-step explanation. This problem covers key logarithmic properties, making it suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation