The image contains mathematical questions in Indonesian, focusing on logarithms and powers. Here is an analysis and solution for each question:

Question 4

The question instructs to "convert to logarithmic form." The options are:

• (a) $5^4$
• (b) $\sqrt[3]{64}$
• (c) $4^3 \cdot 4^3 : 4^4$
• (d) $3^{\frac{9}{2}} : \sqrt{243}$

Solution: To convert expressions into logarithmic form, we identify the powers and try to represent them as logarithmic equations. For example, if $a^b = c$, the logarithmic form is $\log_a c = b$.

Each answer needs individual conversion to logarithmic form.

Question 5

This question says, "Look in the logarithmic table or use a calculator for the following logarithmic values":

• (a) $\log 9$
• (b) $\log 17$
• (c) $\log 5^8$
• (d) $\log 6 : 2$

Solution: Calculating each logarithmic value:

• $\log 9 = 2\log 3$
• $\log 5^8 = 8\log 5$
• Division inside a logarithm $\log \frac{6}{2} = \log 3$.

Question 6

This question states, "If $x$ and $y$ are each 100 and 50, calculate":

• (a) $\log xy$
• (b) $\log \frac{x}{y}$
• (c) $\log x^2 y$
• (d) $\log x^2$

Solution:

• (a) $\log xy = \log(100 \cdot 50) = \log 5000$.
• (b) $\log \frac{x}{y} = \log \frac{100}{50} = \log 2$.
• (c) $\log x^2 y = 2\log x + \log y$.
• (d) $\log x^2 = 2\log x$.

Would you like more detailed explanations for each solution?

Here are 5 related questions to explore further:

1. What are the rules of logarithmic operations?
2. How can we simplify expressions involving powers and logarithms?
3. How do we calculate logarithms of values without a calculator?
4. What are some real-life applications of logarithms?
5. Why is understanding exponentials important in logarithmic problems?

Tip: Remember, converting between exponential and logarithmic forms requires knowing that $a^b = c$ can be rewritten as $\log_a c = b$.