What is the inverse of $y=2log(3x-1)-log(x)$ ?

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Answer 1 · 2015-12-09T15:10:47

$f^-1(x) = frac{ 10^x + 6 ± sqrt {10^x (10^x + 12)}}{18}$

We want x such that $log 10^y = log frac{(3x -1 )^2}{x}, 3x - 1 >0, x> 0$

$10^y * x = 9x^2 - 6x + 1$

$0 = 9x^2 - bx + 1 ; b = 10^y + 6$

$Delta = b^2 - 36 = 10^(2y) + 12 * 10^y$

$x = frac{b ± sqrt Delta}{18} > 1/3$

$b ± sqrt Delta > 6$

$± sqrt Delta > -10^y$

What is the inverse of y=2log(3x-1)-log(x) y=2log(3x-1)-log(x)?