2020 · Q43
If 6³⁻⁴ˣ ⋅ 4ˣ⁺⁵ = 8 (Given log₁₀2 = 0.301 and log₁₀3 = 0.477), then which one of the following is correct?
Elementary MathematicsAlgebra
- A0 < x < 1
- B1 < x < 2
- C2 < x < 3
- D3 < x < 4
Explanation
Taking log10: (3-4x)(0.778)+(x+5)(0.602) = 0.903, which solves to x ~= 1.77. Thus 1 < x < 2 - option (B). A quick check with x = 1.77: 6^(3-7.08)*4^(6.77) ~= 8, confirming the root lies between 1 and 2.