Find the values of satisfying ( _3 [3] 3x + _x [3] 3x ) _3x^3 + ( _3 [3] x 3 + _x [3]…

MATHEMATICS · Subjective · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Find the values of

x

satisfying

\sqrt{\left(\log_3\sqrt[3]{3x}+\log_x\sqrt[3]{3x}\right)\log_3x^3}+\sqrt{\left(\log_3\sqrt[3]{\frac{x}{3}}+\log_x\sqrt[3]{\frac{3}{x}}\right)\log_3x^3}=2.