https://file.aiquickdraw.com/mathbot/file/1726066246147i1kgnzcb.jpg

From the image, we are given the following equations:

1. \( x \cdot \log w = \frac{1}{2} \)
2. \( x \cdot y \cdot \log w = \frac{2}{5} \)

We are asked to find the value of \( y \cdot \log w \).

### Step 1: Solve for \( \log w \) from the first equation

From the first equation:
\[
x \cdot \log w = \frac{1}{2}
\]
Solving for \( \log w \):
\[
\log w = \frac{1}{2x}
\]

### Step 2: Substitute \( \log w \) into the second equation

The second equation is:
\[
x \cdot y \cdot \log w = \frac{2}{5}
\]
Substitute \( \log w = \frac{1}{2x} \) into the equation:
\[
x \cdot y \cdot \frac{1}{2x} = \frac{2}{5}
\]
Simplify:
\[
y \cdot \frac{1}{2} = \frac{2}{5}
\]
Solve for \( y \):
\[
y = \frac{2}{5} \cdot 2 = \frac{4}{5}
\]

### Step 3: Calculate \( y \cdot \log w \)

Now that we know \( y = \frac{4}{5} \) and \( \log w = \frac{1}{2x} \), let's calculate \( y \cdot \log w \):
\[
y \cdot \log w = \frac{4}{5} \cdot \frac{1}{2x} = \frac{4}{10x} = \frac{2}{5x}
\]

Therefore, the value of \( y \cdot \log w \) is \( \frac{2}{5x} \).

---

Would you like further clarification or details on any step? Here are five related questions for practice:

1. How do you isolate \( x \) in the equation \( x \log w = \frac{1}{2} \)?
2. If \( y = \frac{1}{2} \), how would the second equation change?
3. What happens to the equation if \( x = 2 \)?
4. How can logarithmic identities be applied in solving such equations?
5. What is the significance of \( \log w \) when \( w \) is a constant?

**Tip:** When solving logarithmic equations, isolating variables step by step is crucial for accuracy.

Jika x log w = 1/2 dan x y log w = 2/5, maka nilai y log w = ?

Solve the logarithmic problem where x log w = 1/2 and x y log w = 2/5, and find the value of y log w using algebraic manipulation and properties of logarithms. Suitable for high school students in Grades 9-12.

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