The expression shown in the image is:

$2\log 3 + 3\log 2$

This can be simplified by using the logarithm power rule, which states that $a \log b = \log b^a$. Applying this rule:

$2\log 3 + 3\log 2 = \log 3^2 + \log 2^3 = \log 9 + \log 8$

Next, use the logarithm addition rule, which states that $\log a + \log b = \log (a \times b)$:

$\log 9 + \log 8 = \log (9 \times 8) = \log 72$

So, the simplified expression is:

$\log 72$

Would you like more details or have any questions?

Here are five related questions:

1. How would the expression change if the original problem was $2\log 3 + 3\log 4$?
2. What is the base of the logarithms used here, and how would it change the result if it were different?
3. How can this result be verified using a calculator?
4. What is the interpretation of $\log 72$ in terms of powers of 10?
5. How would you solve $2\log x + 3\log y$ in terms of $x$ and $y$?

Tip: Remember that simplifying logarithmic expressions often involves applying the power and product rules of logarithms.