I have the multivariable function \log(y^2+4x^2-4) and I have found the maximal

I have the multivariable function
$$\displaystyle{\log{{\left({y}^{{2}}+{4}{x}^{{2}}-{4}\right)}}}$$
and I have found the maximal domain to be
$$\displaystyle{x}^{{2}}+{\frac{{{y}^{{2}}}}{{{4}}}}{>}{1}$$

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Durst37
We have
$$\displaystyle{\ln{:}}{\left({0},\infty\right)}\rightarrow\mathbb{R}$$
and $$\displaystyle{\ln{:}}{\left({1},\infty\right)}\rightarrow\mathbb{R}^{+}-{\left\lbrace{0}\right\rbrace}$$
Not exactly what you’re looking for?
turtletalk75
Take y=0. Then you can study the range of the function of one variable. Once you got it you will know the range of the multivariable function