https://file.aiquickdraw.com/mathbot/file/1730273015020rfnkgw2c.jpg

To solve the equation provided in the image:

\[
5^{3 - x} = \frac{1}{(25 - 3)^{x + 3}}
\]

we can follow these steps:

1. **Rewrite the Terms**: Simplify \((25 - 3)\) in the denominator.
   \[
   25 - 3 = 22
   \]
   So the equation becomes:
   \[
   5^{3 - x} = \frac{1}{22^{x + 3}}
   \]

2. **Express in Terms of Exponents**: Write \( \frac{1}{22^{x+3}} \) as \( 22^{-(x+3)} \).
   \[
   5^{3 - x} = 22^{-(x + 3)}
   \]

3. **Compare Exponents**: Since the bases (5 and 22) are not the same, we need to analyze further to solve for \( x \). In this case, there is no direct way to solve this algebraically because the bases differ, which suggests we may need logarithms or numerical approximation.

Would you like me to proceed with solving it numerically or discuss other approaches? 

### Additional Related Questions
1. How would the solution change if the bases on both sides were the same?
2. Can logarithmic properties help simplify cases like this?
3. What techniques are useful for equations with different exponential bases?
4. How does changing the exponent sign affect the solution?
5. Could this equation be graphed to find an approximate solution?

#### Tip:
For equations with exponents on both sides but different bases, consider taking logarithms to simplify

Nilai x yang memenuhi 5^(3-x) = 1/(25-3)^(x+3)

Learn how to solve the exponential equation 5^(3 - x) = 1/(25 - 3)^(x + 3) by simplifying terms, converting exponents, and using logarithmic properties for further analysis. This problem covers key concepts in solving exponential equations and is suitable for students in Grades 10-12.

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