Solve the exponential equation.

52x = 57
		17.5
		-3.5
		3.5
		5


We have the exponential equation:

\[
5^{2x} = 5^7
\]

Since the bases are the same (both are 5), we can set the exponents equal to each other. This gives us:

\[
2x = 7
\]

Now, solve for \(x\):

\[
x = \frac{7}{2} = 3.5
\]

Thus, the solution is \(x = 3.5\).

Would you like more details, or do you have any questions?

Here are 5 related questions to expand on this:

1. How do you solve exponential equations when the bases are not the same?
2. What happens when you have an exponential equation with different bases?
3. Can exponential functions have negative solutions?
4. How do logarithms help in solving more complex exponential equations?
5. What is the general process for solving exponential growth problems?

**Tip:** When the bases are the same in an exponential equation, you can set the exponents equal and solve for the unknown.

Solve the exponential equation: 5^(2x) = 5^7

Learn how to solve the exponential equation 5^(2x) = 5^7 by equating exponents when the bases are the same. This detailed step-by-step solution demonstrates core algebraic concepts like exponential equations and exponent laws. Ideal for students in Grades 9-10.

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