Algebra-2

Question Analysis
This question involves solving an exponential equation with a fraction on one side, which requires using negative exponents.
The main focus is on rewriting the fraction as a power of the base (5) with a negative exponent and then equating exponents.

Key Concept Explanation
A negative exponent indicates the reciprocal of the base raised to the positive exponent: (where , , is a real number). This allows us to rewrite fractions as powers of the original base, enabling the use of the One-to-One Property.

Step-by-Step Solution
1. Rewrite using a negative exponent with base 5: .
2. Substitute back into the equation: .
3. Apply the One-to-One Property: Set exponents equal: .
4. Solve for : Divide both sides by 2:

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