Oh ok... then you can have this simple
use-only-simple-rules-no-calculator solution then :)
(2/x)^2logn2 = (3/x)^2logn3
Taking log to base n on both sides
logn(2/x)^2logn2 = (3/x)^2logn3
2logn2[logn2-lognx] = 2logn3[logn3-lognx]
logn2[logn2-lognx] = logn3[logn3-lognx]
(logn2)^2 -(logn2)(lognx) = (logn3)^2 - (logn3)(lognx)
(logn3)(lognx)-(logn2)(lognx) = (logn3)^2-(logn2)^2
lognx[logn3-logn2] = (logn3-logn2)(logn3+logn2)
lognx = logn3 + logn2
lognx = logn6
x =6
Same method as uncertain's probably. But just for the benefit of
those who need it step by step. Does not make use of uncommon
concepts. Only make use of 2 simple concepts.
1. Must have same base.
2. Making whatever contain x the subject. (E Maths)