Solve for X

$${\frac{{{log}}_{{\mathtt{2}}}{\left({\mathtt{4\,096}}\right)}}{{{log}}_{{\mathtt{x}}}{\left({\frac{{\mathtt{37}}}{{\mathtt{999}}}}\right)}}} = -{\mathtt{4}}$$

$${{log}}_{{\mathtt{2}}}{\left({\mathtt{4\,096}}\right)} = {\mathtt{12}}$$

$${\frac{{\mathtt{12}}}{{{log}}_{{\mathtt{x}}}{\left(\left({\frac{{\mathtt{37}}}{{\mathtt{999}}}}\right)\right)}}} = -{\mathtt{4}}$$

$${\mathtt{12}} = {\mathtt{\,-\,}}\left({\mathtt{4}}{\mathtt{\,\times\,}}{{log}}_{{\mathtt{x}}}{\left({\frac{{\mathtt{37}}}{{\mathtt{999}}}}\right)}\right)$$

$$-{\mathtt{3}} = {{log}}_{{\mathtt{x}}}{\left({\frac{{\mathtt{37}}}{{\mathtt{999}}}}\right)}$$

$${{\mathtt{x}}}^{-{\mathtt{3}}} = {\frac{{\mathtt{37}}}{{\mathtt{999}}}}$$

$${\frac{{\mathtt{1}}}{{{\mathtt{x}}}^{{\mathtt{3}}}}} = {\frac{{\mathtt{37}}}{{\mathtt{999}}}}$$

$${\mathtt{999}} = {\mathtt{37}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{3}}}$$

$${\mathtt{27}} = {{\mathtt{x}}}^{{\mathtt{3}}}$$

$${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{27}}}} = {\mathtt{x}}$$

$${\mathtt{x}} = {\mathtt{3}}$$

See Anonymous's answer below.