# What is the inverse of y = log_3 (4x^2-4)  ?

$y = \pm \sqrt{\frac{{3}^{x} + 4}{4}}$

#### Explanation:

From the given equation $y = {\log}_{3} \left(4 {x}^{2} - 4\right)$

Interchange the variables, then solve for $x$

$x = {\log}_{3} \left(4 {y}^{2} - 4\right)$

${3}^{x} = {3}^{{\log}_{3} \left(4 {y}^{2} - 4\right)}$

$y = \pm \sqrt{\frac{{3}^{x} + 4}{4}}$

God bless ....I hope the explanation is useful.