https://file.aiquickdraw.com/mathbot/file/1727378496695l80tely3.jpg

The question in the image is asking to solve for the value of \( 9^x \), given that:

\[
15^x = 5^{x+1}
\]

### Step 1: Rewrite the equation in terms of base 5.
We can express \( 15 \) as \( 3 \times 5 \), so the given equation becomes:

\[
(3 \times 5)^x = 5^{x+1}
\]

Using the property of exponents, \( (ab)^x = a^x \times b^x \), this simplifies to:

\[
3^x \times 5^x = 5^{x+1}
\]

### Step 2: Simplify the equation.
Cancel out \( 5^x \) from both sides:

\[
3^x = 5
\]

### Step 3: Solve for \( x \).
Take the natural logarithm (ln) of both sides:

\[
x \ln(3) = \ln(5)
\]

Thus, \( x \) is:

\[
x = \frac{\ln(5)}{\ln(3)}
\]

### Step 4: Find the value of \( 9^x \).
We know that \( 9 = 3^2 \), so:

\[
9^x = (3^2)^x = 3^{2x}
\]

Since \( x = \frac{\ln(5)}{\ln(3)} \), we substitute this value:

\[
9^x = 3^{2 \times \frac{\ln(5)}{\ln(3)}} = 5^2 = 25
\]

Thus, the value of \( 9^x \) is \( \boxed{25} \).

---

Would you like more details or have any questions about this solution?

Here are 5 related questions for further practice:

1. How would you solve \( 27^x = 9^{x+1} \)?
2. Can you solve \( 5^{2x} = 25^{x+1} \) for \( x \)?
3. What happens if \( 3^x = 4 \)? How would you solve for \( x \)?
4. Can you find \( 9^x \) if \( 4^x = 16 \)?
5. Solve \( 2^{3x} = 32 \).

**Tip:** When solving exponential equations, using logarithms is often the key to isolating the variable in the exponent!

Given that 15^x = 5^(x+1), find the value of 9^x.

Learn how to solve the exponential equation 15^x = 5^(x+1) and find the value of 9^x. This solution involves the use of exponent laws and logarithms, suitable for students in Grades 10-12.

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