Question Number 32954 by mondodotto@gmail.com last updated on 07/Apr/18
$$\:\boldsymbol{\mathrm{log}}_{\mathrm{2}} \boldsymbol{{x}}×\boldsymbol{\mathrm{log}}_{\mathrm{4}} \boldsymbol{{x}}×\boldsymbol{\mathrm{log}}_{\mathrm{16}} \boldsymbol{{x}}=\mathrm{7} \\ $$$$\:\boldsymbol{{help}} \\ $$
Answered by MJS last updated on 08/Apr/18
$$\mathrm{log}_{\mathrm{2}} \:{x}×\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}_{\mathrm{2}} \:{x}×\frac{\mathrm{1}}{\mathrm{4}}\mathrm{log}_{\mathrm{2}} \:{x}=\mathrm{7} \\ $$$$\frac{\mathrm{1}}{\mathrm{8}}\left(\mathrm{log}_{\mathrm{2}} \:{x}\right)^{\mathrm{3}} =\mathrm{7} \\ $$$$\mathrm{log}_{\mathrm{2}} \:{x}=\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{7}} \\ $$$${x}=\mathrm{2}^{\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{7}}} =\mathrm{4}^{\sqrt[{\mathrm{3}}]{\mathrm{7}}} \approx\mathrm{14}.\mathrm{18075} \\ $$