if you add and minus logs do you divide and multiply them

Yes, when you add or subtract logarithms, you're essentially multiplying or dividing the values inside the logarithms. This process is based on the logarithmic properties:

### 1. **Addition of Logs:**
When you add logarithms with the same base, it translates into multiplying the arguments inside the logs:
\[
\log_b(A) + \log_b(B) = \log_b(A \cdot B)
\]

For example:
\[
\log_2(4) + \log_2(8) = \log_2(4 \times 8) = \log_2(32)
\]

### 2. **Subtraction of Logs:**
When you subtract logarithms with the same base, it means you're dividing the arguments inside the logs:
\[
\log_b(A) - \log_b(B) = \log_b\left(\frac{A}{B}\right)
\]

For example:
\[
\log_2(8) - \log_2(4) = \log_2\left(\frac{8}{4}\right) = \log_2(2)
\]

### Key Points:
- Addition of logs becomes multiplication.
- Subtraction of logs becomes division.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do logarithmic properties apply to exponents?
2. Can logarithms with different bases be added or subtracted?
3. What is the inverse operation of logarithms?
4. How does the change of base formula work for logarithms?
5. What happens when you multiply or divide logarithms directly?

**Tip:** Remember that logarithms only work with positive numbers inside them—negative or zero arguments are undefined!

This page explains how adding and subtracting logarithms corresponds to multiplying and dividing the arguments inside the logs. Explore the properties of logarithms with examples, including key formulas for log addition and subtraction. Suitable for students in Grades 9-12.

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