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The given expression is:

\[
\log_3(a) + \log_3(a + 3)
\]

To combine these into a single logarithm, we use the logarithmic property:

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

Applying this property to the expression:

\[
\log_3(a) + \log_3(a + 3) = \log_3(a \cdot (a + 3))
\]

This simplifies to:

\[
\log_3(a(a + 3)) = \log_3(a^2 + 3a)
\]

Thus, the final answer is:

\[
\log_3(a^2 + 3a)
\]

Let me know if you need further clarification!

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**Related Questions:**

1. How do you solve logarithmic equations using the properties of logarithms?
2. Can the sum of logarithms with different bases be simplified in the same way?
3. What happens when you subtract logarithms instead of adding them?
4. How do you expand a single logarithmic expression into multiple terms?
5. How do you evaluate \(\log_3(a)\) when \(a\) is given?

**Tip:** Always ensure the argument of a logarithmic function is positive, as logarithms are only defined for positive numbers.

Write the following sum as a single logarithm: log_3(a) + log_3(a + 3).

Learn how to simplify the sum log_3(a) + log_3(a + 3) into a single logarithmic expression using the product rule for logarithms. This guide covers essential concepts of logarithms and algebra, suitable for students in Grades 9-11.

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