Problem 18 - Entrance Test

If 2ˣ = 3ˣ⁺¹, find x.

A. log₂3B. log₂3 + 1C. log₂3 - 1D. 1/(log₃2 - 1)E. log₂3/(1 - log₃2)

Correct: E

Take ln: x ln2 = (x+1) ln3 → x(ln2 - ln3) = ln3 → x = ln3/(ln2 - ln3) = log₂3/(1 - log₃2).