Advanced MathHardExponential equation whose exponents form a quadratic
Advanced Math practice question
If 3^(x²) = 3^(5x − 6), what is the sum of all possible values of x?
Answer: 5
Equal bases give equal exponents: x² = 5x − 6 → x² − 5x + 6 = 0 → (x − 2)(x − 3) = 0. The values are 2 and 3, whose sum is 5.
Common wrong answers
- If you answered 2
- 2 is one of the values.
- If you answered 6
- 6 is the product of the values.
- If you answered -5
- −5 has the wrong sign; the sum of the roots of x² − 5x + 6 is +5.
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