https://file.aiquickdraw.com/mathbot/file/17267200423681576ta45.jpg

The image contains two logarithmic problems written in Indonesian. I will translate and solve them:

**Problem 2:**
"Tentukan nilai dari \( ^5\log 15 + ^5\log 5 - ^5\log 3 \) menggunakan sifat 1, 3, 4, dan 5."

Translation:
Find the value of \( \log_5{15} + \log_5{5} - \log_5{3} \) using properties 1, 3, 4, and 5.

**Solution:**
Using logarithmic properties:

1. **Property 1 (Product rule):**  
   \(\log_b(xy) = \log_b{x} + \log_b{y}\)

2. **Property 2 (Quotient rule):**  
   \(\log_b{\frac{x}{y}} = \log_b{x} - \log_b{y}\)

Now, simplifying:

\[
\log_5{15} + \log_5{5} - \log_5{3}
\]

Step 1: \( \log_5{15} = \log_5{(3 \times 5)} = \log_5{3} + \log_5{5} \)

Step 2: Substitute this into the original expression:

\[
(\log_5{3} + \log_5{5}) + \log_5{5} - \log_5{3}
\]

Step 3: Simplify:

\[
\log_5{3} + \log_5{5} + \log_5{5} - \log_5{3}
\]

The \( \log_5{3} \)'s cancel out, leaving:

\[
\log_5{5} + \log_5{5}
\]

Step 4: We know that \( \log_5{5} = 1 \), so:

\[
1 + 1 = 2
\]

**Answer for Problem 2:**
The value is \( 2 \).

---

**Problem 3:**
"Tentukan nilai dari \( ^7\log 3 \cdot ^5\log 49 \cdot ^9\log 25 \) menggunakan sifat 1, 5, dan 9."

Translation:
Find the value of \( \log_7{3} \cdot \log_5{49} \cdot \log_9{25} \) using properties 1, 5, and 9.

**Solution:**
This involves three logarithmic terms. We'll need to break these down and simplify where possible.

1. **Logarithmic form of powers:**  
   Use \( \log_b{x^k} = k \log_b{x} \)

Let's break down each logarithm:

\[
\log_7{3}, \quad \log_5{49} = \log_5{(7^2)} = 2 \log_5{7}, \quad \log_9{25} = \log_9{(5^2)} = 2 \log_9{5}
\]

So the expression becomes:

\[
\log_7{3} \cdot 2 \log_5{7} \cdot 2 \log_9{5}
\]

Now, without specific values for \( \log_7{3} \), \( \log_5{7} \), and \( \log_9{5} \), we can't simplify this further arithmetically without a calculator. However, this is the most simplified form using the logarithmic properties given.

**Answer for Problem 3:**
The simplified expression is:

\[
2 \log_7{3} \cdot 2 \log_5{7} \cdot \log_9{5}
\]

---

Would you like any further details on these solutions or clarifications on logarithmic properties?

### Related Questions:
1. How do you apply the change of base formula to logarithmic expressions?
2. What is the logarithmic property for powers, and how can it simplify calculations?
3. How does the quotient rule for logarithms work?
4. Can you explain how to calculate the values of \(\log_7{3}\), \(\log_5{7}\), and \(\log_9{5}\) using a calculator?
5. How can the product and quotient rules for logarithms be combined to solve more complex problems?

### Tip:
Always try to simplify logarithmic expressions by applying the basic properties (product, quotient, and power rules) before calculating specific values.

Tentukan nilai dari log 15 + log 5 - log 3 menggunakan sifat 1,3,4, dan 5.

This guide explains how to solve logarithmic expressions using the basic properties of logarithms, including the product, quotient, and power rules. Learn how to simplify and calculate the expression log(15) + log(5) - log(3) step-by-step, suitable for high school students in Grades 10-12.

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