Question Number 49691 by Rio Michael last updated on 09/Dec/18
$${simplify}\:\frac{{log}_{\mathrm{3}} \mathrm{64}\:×\:{log}_{\mathrm{4}} \mathrm{243}}{{log}_{\mathrm{2}} \mathrm{16}} \\ $$
Answered by math1967 last updated on 09/Dec/18
$$\frac{{log}_{\mathrm{3}} \mathrm{4}^{\mathrm{3}} ×{log}_{\mathrm{4}\:} \mathrm{3}^{\mathrm{5}} }{{log}_{\mathrm{2}} \mathrm{2}^{\mathrm{4}} }=\frac{\mathrm{3}{log}_{\mathrm{3}\:\:} \mathrm{4}×\mathrm{5}{log}_{\mathrm{4}} \mathrm{3}}{\mathrm{4}{log}_{\mathrm{2}} \mathrm{2}} \\ $$$$=\frac{\mathrm{3}×\mathrm{5}{log}_{\mathrm{3}} \mathrm{4}×{log}_{\mathrm{4}} \mathrm{3}}{\mathrm{4}×\mathrm{1}}=\frac{\mathrm{15}×\mathrm{1}}{\mathrm{4}}=\mathrm{3}.\mathrm{75}{ans} \\ $$