Theory question 102
Indices and LogarithmsGiven that log3 x − 3logx 3 + 2 = 0, find the values of x.
Show the model answer
Model answer
Let t = log₃ x; then log_x 3 = 1/t.
t − 3/t + 2 = 0, so t² + 2t − 3 = 0, (t + 3)(t − 1) = 0.
t = 1: x = 3. t = −3: x = 3⁻³ = 1/27.
Explanation
log_x 3 is the reciprocal of log₃ x.