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The question asks to calculate the value of \( M = 3^{\log_2{a}} \), where \( a > 0 \).

We can use the following logarithmic property to simplify the expression:

\[
x^{\log_b{y}} = y^{\log_b{x}}
\]

Applying this to \( M = 3^{\log_2{a}} \):

\[
M = a^{\log_2{3}}
\]

Now, \( \log_2{3} \) is a constant, but the final expression simplifies to \( a^{\log_2{3}} \). Since none of the options explicitly include this form, it is likely that an approximation or simplified form of this is expected. 

If approximating \( \log_2{3} \approx 1.585 \), then the value would be approximately \( M \approx a^{1.585} \). But we will stick to the simplified symbolic form.

In conclusion:
- The answer involves rewriting \( M = a^{\log_2 3} \).

If you'd like me to check further or clarify, feel free to ask.

Do you have any questions or would like additional details?

### Related Questions:
1. How can we use logarithmic properties to simplify expressions involving different bases?
2. What is the significance of logarithmic change of base?
3. Can \( \log_2{3} \) be estimated without a calculator?
4. How does \( a^{\log_b{c}} \) differ from regular exponential expressions?
5. How do logarithmic functions apply to growth models in real-world scenarios?

**Tip**: Always check if logarithmic identities or approximations are needed based on multiple-choice options.

Với a > 0, tính M = 3^{\log_2{a}} theo a.

Learn how to simplify the expression M = 3^{\log_2{a}} using logarithmic identities and the change of base formula. This problem covers key concepts in exponential and logarithmic functions, suitable for students in Grades 10-12.

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