Solve for exact value of x for (3x)^lg3 = (4x)^lg 4

[Ans = 1/12]

I took lg on both sides and rearranged to get

lg 3x / lg 4x = lg 4 / lg 3

lg 3x / lg 4x = 1.262 (evaluate)

lg 3x = 1.262 lg 4x (Cross-multiply)

lg 3x - lg 4x^1.262 = 0

lg (3x/4x^1.262) = 10^0

3x = 4x^1.262

3/4 = x^1.262 / x

Solving, x = 3/4^(1/0.262) = 0.334

Please advise where I went wrong with my working, coz my answers' not right!

Thanks !