Use the properties of logarithms to simplify the expression.
9log9(11)


The given expression is:

\[
9 \log_9 (11)
\]

We can simplify this expression using the **power rule** of logarithms. The power rule states:

\[
a \log_a (x) = x
\]

In this case, \( a = 9 \), so applying the rule:

\[
9 \log_9 (11) = 11
\]

Thus, the simplified expression is:

\[
11
\]

Would you like more details or have any questions? Here are five related questions you might want to explore:

1. How do you simplify \( 5 \log_5 (25) \)?
2. What is the value of \( 2 \log_2 (8) \)?
3. How do logarithms with different bases affect simplification?
4. Can the expression \( \log_b (b^x) \) be simplified further?
5. How would you solve \( 3 \log_3 (27) \)?

**Tip**: When the base of a logarithm matches the coefficient, the expression simplifies directly to the argument inside the logarithm.

Use the properties of logarithms to simplify the expression 9log9(11).

Learn how to simplify the expression 9log9(11) using the power rule of logarithms. This step-by-step solution demonstrates how to apply the property of logarithms to reduce the expression to 11. Suitable for students in Grades 9-11, covering key logarithmic concepts.

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