Solve for x in the equation \(5^{x} \times 5^{x + 1} = 25\).
FURTHER MATHEMATICS
WAEC 2016
Solve for x in the equation \(5^{x} \times 5^{x + 1} = 25\).
- A. \(-2\)
- B. \(\frac{-1}{2}\)
- C. \(\frac{1}{2}\)
- D. \(2\)
Correct Answer: C. \(\frac{1}{2}\)
Explanation
\(5^{x} \times 5^{x+1} = 25\)
\(5^{x} \times 5^{x+1} = 5^{2}\)
\(5^{x+x+1} = 5^{2}\), equating powers,
\(2x + 1 = 2 \implies 2x = 1\)
\(\therefore x = \frac{1}{2}\)
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