Advanced MathMediumExponent equation with a linear exponent
Advanced Math practice question
If 3^(2x − 1) = 2,187, what is the value of x? (Note: 2,187 = 3⁷.)
Answer: 4
Since 2,187 = 3⁷, the exponents must match: 2x − 1 = 7, so 2x = 8 and x = 4.
Common wrong answers
- If you answered 3
- 3 comes from 2x − 1 = 5, a slip in identifying the power (2,187 is 3⁷, not 3⁵).
- If you answered 7
- 7 is the exponent on 3, which equals 2x − 1, not x.
- If you answered 4.5
- 4.5 comes from 2x = 9 — the −1 was subtracted from 7 rather than added: 7 + 1 = 8.
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