To solve the expression:

\[
\log_3(15) + \log_3\left(\frac{9}{5}\right)
\]

we can use the logarithmic property:

\[
\log_b(x) + \log_b(y) = \log_b(x \cdot y)
\]

So, applying this property:

\[
\log_3(15) + \log_3\left(\frac{9}{5}\right) = \log_3\left(15 \cdot \frac{9}{5}\right)
\]

Now, simplify the multiplication:

\[
15 \cdot \frac{9}{5} = \frac{15 \cdot 9}{5} = 27
\]

Thus, the expression simplifies to:

\[
\log_3(27)
\]

Since \( 3^3 = 27 \), we know:

\[
\log_3(27) = 3
\]

So the final answer is:

\[
\boxed{3}
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you simplify expressions involving logarithms with different bases?
2. What are the general properties of logarithms that can be used for simplifications?
3. Can you evaluate \(\log_3(81)\)?
4. How does changing the base of a logarithm affect the calculation?
5. How do you convert a logarithmic expression to an exponential one?

**Tip:** Remember, logarithms convert multiplication into addition, and exponentiation into multiplication!

Learn how to simplify the logarithmic expression log_3(15) + log_3(9/5) using logarithmic properties. This step-by-step guide breaks down the multiplication of fractions and the logarithmic addition rule to find the solution. Suitable for students in Grades 9-11.

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