Question

Solve log2(x – 1) = log12(x – 1) by graphing.
x =

Answer 1

Using change of base: log2(x−1) = ln(x−1)/ln2 and log12(x−1) = ln(x−1)/ln12. So
ln(x−1)/ln2 = ln(x−1)/ln12
=> ln(x−1) (1/ln2 − 1/ln12) = 0.

Since 1/ln2 ≠ 1/ln12, we must have ln(x−1) = 0 → x−1 = 1 → x = 2.

(Also by graphing: both y = log2(x−1) and y = log12(x−1) pass through (2,0) and, being increasing, intersect only there.)