2021 · Q55
If 5ˣ⁻³ = 8, then what is x equal to?
Elementary MathematicsAlgebra
- A3/(1 − log₁₀ 2)
- B3/(1 + log₁₀ 2)
- C2/(1 − log₁₀ 2)
- D5/(1 − log₁₀ 2)
Explanation
Taking logs: (x−3)·log 5 = log 8 = 3log 2. Since log 5 = 1 − log 2, x − 3 = 3log2/(1−log2), so x = [3(1−log2) + 3log2]/(1−log2) = 3/(1−log₁₀2). Hence option A.