https://file.aiquickdraw.com/mathbot/file/1725470081445rvioihy7.jpg

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?

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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.

Learn how to simplify the logarithmic expression 2log3 + 3log2 using the logarithm power and addition rules. This step-by-step solution covers key logarithmic concepts and is suitable for students in Grades 9-12.

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