a log 1 : 0
a log x : 1
log x : ¹⁰log x
a log x • y : a log x + a log y
a log x/y : a log x - a log y
a log x • x log y • y log z : a log z
a log x pangkat n : n • log x
a pangkat n log x : 1/n kali a log x
a pangkat n log x pangkat m : m/n kali a log x
a log x : b log x/b log a
a log x : 1 tidak sama dengan x
a pangkat a log x : x

The statements you've shared appear to be a mix of logarithmic properties and identities. I will clarify them and restate the correct logarithmic rules based on your input.

1. **\( \log_a 1 = 0 \)**  
   - This is true because any logarithm of 1, regardless of the base, is always 0.

2. **\( \log_a x = 1 \) when \( x = a \)**  
   - This means that the logarithm of a number \( x \) in base \( a \) is 1 if and only if \( x = a \). For example, \( \log_2 2 = 1 \).

3. **\( \log x = \log_{10} x \)**  
   - This indicates that if no base is specified, it is implied to be base 10 (common logarithm).

4. **Product Rule**: \( \log_a (x \cdot y) = \log_a x + \log_a y \)  
   - When multiplying numbers inside a logarithm, you can separate them into a sum of two logarithms.

5. **Quotient Rule**: \( \log_a \left( \frac{x}{y} \right) = \log_a x - \log_a y \)  
   - When dividing numbers inside a logarithm, you can separate them into a difference of two logarithms.

6. **Multiple Terms**: \( \log_a (x \cdot x \cdot y \cdot y \cdot z) = \log_a z \)  
   - This could be interpreted as combining multiple terms into one logarithm, though the logic might be unclear without more context.

7. **Power Rule**: \( \log_a (x^n) = n \cdot \log_a x \)  
   - When raising a number inside a logarithm to a power, you can pull the exponent out in front.

8. **Logarithmic Base and Power Rule**:  
   \( \log_{a^n} x = \frac{1}{n} \cdot \log_a x \)  
   - If the base of a logarithm is raised to a power \( n \), you can factor out \( \frac{1}{n} \).

9. **Another Power Rule**:  
   \( \log_{a^n} (x^m) = \frac{m}{n} \cdot \log_a x \)  
   - This is a generalization of the previous rule combining both powers inside and outside the logarithm.

10. **Change of Base Formula**:  
   \( \log_a x = \frac{\log_b x}{\log_b a} \)  
   - This is the change of base formula, which allows you to change the base of a logarithm to another base \( b \).

11. **\( \log_a x \neq 1 \text{ if } x \neq a \)**  
   - This is stating that \( \log_a x \) will not equal 1 unless \( x = a \).

12. **Exponent-Log Rule**:  
   \( a^{\log_a x} = x \)  
   - This is the inverse property of logarithms. If a number is raised to its own logarithmic base, the result is \( x \).

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### Do you have any specific questions about these properties or would you like further clarification on one of them?

### 5 Related Questions:
1. How do you apply the change of base formula in solving logarithmic equations?
2. What are some real-life applications of logarithmic functions?
3. Can you explain the difference between natural logarithms and common logarithms?
4. How does the power rule simplify logarithmic expressions?
5. What happens when you raise a logarithmic function to a power?

### Tip: When working with logarithms, always check if you can apply logarithmic properties (product, quotient, or power rules) to simplify expressions before solving them.

Understand key logarithmic properties such as the product, quotient, and power rules through detailed formulas and examples. Learn how to apply the change of base formula and other important logarithmic rules. Suitable for students in Grades 9-12.

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