Multiple choice

Solve the following equation for $x:125={5}^{2x-1}$.

  1. $2$
  2. $5$
  3. $\sqrt 5$
  4. $25$
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A Correct answer
Explanation

125 = 5^3. So 5^3 = 5^(2x-1). Equating exponents: 3 = 2x - 1, 4 = 2x, x = 2.

AI explanation

Express both sides of the equation with the same base to write 125 as 5^3, giving 5^3 = 5^(2x - 1). Since the bases are the same, set the exponents equal to each other: 3 = 2x - 1. Add 1 to both sides to get 4 = 2x, so x = 2.

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