https://file.aiquickdraw.com/mathbot/file/1726734054449amnrx3g4.jpg

The image contains a set of logarithmic problems. Let's solve the problems shown:

### Question a:
\[
\log_3 243
\]
We need to find \( \log_3 243 \), which means we are solving for \( x \) in the equation:
\[
3^x = 243
\]
We know that \( 243 = 3^5 \), so:
\[
\log_3 243 = 5
\]

### Question b:
\[
\log_5 25\sqrt{5}
\]
This can be simplified as:
\[
\log_5 \left(25 \times \sqrt{5}\right) = \log_5 \left(5^2 \times 5^{1/2}\right)
\]
Using the logarithmic property \( \log_b (a \times c) = \log_b a + \log_b c \), we get:
\[
\log_5 \left(5^2 \times 5^{1/2}\right) = \log_5 5^2 + \log_5 5^{1/2}
\]
Since \( \log_5 5^n = n \), we can simplify further:
\[
\log_5 5^2 + \log_5 5^{1/2} = 2 + \frac{1}{2} = 2.5
\]

### Final Answers:
a. \( \log_3 243 = 5 \)  
b. \( \log_5 25\sqrt{5} = 2.5 \)

Would you like further explanations on logarithmic properties or any other details?

Here are 5 related questions:
1. How do you express logarithmic equations in exponential form?
2. What are the properties of logarithms, and how are they applied in solving problems?
3. Can you solve \( \log_2 32 \) using logarithmic properties?
4. How would you solve a logarithmic equation where the base is unknown?
5. What is the change of base formula for logarithms?

**Tip:** Understanding the fundamental properties of logarithms, such as the product, quotient, and power rules, can greatly simplify solving logarithmic expressions.

Tentukan nilai logaritma berikut! a. log_3 243 b. log_5 25√5

Learn how to solve the logarithmic equations log_3 243 and log_5 25√5 using logarithmic properties. Suitable for students in Grades 8-10, this problem explains how to apply product and power rules to logarithmic expressions.

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