Question

Solve the following equation:
${\left({\left(\sqrt[5]{527}\right)}^{x/4-\sqrt{x/3}}\right)}^{x/4+\sqrt{x/3}}=\sqrt{27}$

Answer 1

$((\sqrt[5]{527}{)}^{x/4-\sqrt{x/3}}{)}^{x/4+\sqrt{x/3}}=\sqrt{27}$

$(\sqrt[5]{527}{)}^{(x/4{)}^2-x/3}={27}^{1/2}$

$(x/4{)}^2-x/3=5/2⟹3x^2-16x-120=0⟹x=\frac{16\pm \sqrt{256+1440}}{6}=\frac{8\pm \sqrt{424}}{3}$