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!