https://file.aiquickdraw.com/mathbot/file/1727225067489jtdcx50o.jpg

The equation provided in the image is:

\[
5^{5x + 125} = 25^{5x + 125}
\]

To solve this, notice that \( 25 \) can be written as \( 5^2 \). So, the equation becomes:

\[
5^{5x + 125} = (5^2)^{5x + 125}
\]

Simplifying the right-hand side:

\[
5^{5x + 125} = 5^{2(5x + 125)}
\]

Now that both sides have the same base (\( 5 \)), we can set the exponents equal to each other:

\[
5x + 125 = 2(5x + 125)
\]

Expanding the right-hand side:

\[
5x + 125 = 10x + 250
\]

Now, solve for \( x \):

\[
125 - 250 = 10x - 5x
\]
\[
-125 = 5x
\]
\[
x = -25
\]

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

Would you like a detailed breakdown of any specific part, or do you have further questions?

Here are some related questions to explore:
1. How would the equation change if the base were different?
2. Can this method be applied to other similar exponential equations?
3. How would you solve an equation like \( a^{bx + c} = d^{bx + c} \)?
4. How would the solution change if the exponent had different coefficients for \( x \)?
5. What if both sides of the equation had different bases?

**Tip:** Always check if the numbers in an exponential equation can be expressed with the same base. This simplifies the equation significantly!

Nilai x yang memenuhi 5^{5x + 125} = 25^{5x + 125} adalah.

Learn how to solve the exponential equation 5^{5x + 125} = 25^{5x + 125} with a step-by-step solution. Understand key concepts in algebra, including simplifying exponential expressions and using the equality of exponents theorem. Suitable for students in Grades 10-12.

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