Question Number 25113 by Mr easy last updated on 04/Dec/17
Commented by prakash jain last updated on 05/Dec/17
$$\left(\mathrm{log}_{\mathrm{2}} {x}\right)^{\mathrm{3}} +\left(\mathrm{log}_{\mathrm{2}} {y}\right)^{\mathrm{3}} \\ $$$$=\left(\mathrm{log}_{\mathrm{2}} {x}+\mathrm{log}_{\mathrm{2}} {y}\right)\left[\left(\mathrm{log}_{\mathrm{2}} {x}\right)^{\mathrm{2}} +\left(\mathrm{log}_{\mathrm{2}} {y}\right)^{\mathrm{2}} −\left(\mathrm{log}_{\mathrm{2}} {x}\right)\left(\mathrm{log}_{\mathrm{2}} {y}\right)\right] \\ $$$$=\left(\mathrm{log}_{\mathrm{2}} {xy}\right)\left[\left(\mathrm{log}_{\mathrm{2}} {x}+\mathrm{log}_{\mathrm{2}} {y}\right)^{\mathrm{2}} −\mathrm{3}\left(\mathrm{log}_{\mathrm{2}} {x}\right)\left(\mathrm{log}_{\mathrm{2}} {y}\right)\right] \\ $$$$=\left(\mathrm{log}_{\mathrm{2}} {xy}\right)\left[\left(\mathrm{log}_{\mathrm{2}} {xy}\right)^{\mathrm{2}} −\mathrm{3}\left(\mathrm{log}_{\mathrm{2}} {x}\right)\left(\mathrm{log}_{\mathrm{2}} {y}\right)\right] \\ $$$$=\mathrm{15}\left[\mathrm{15}^{\mathrm{2}} −\mathrm{3}×\mathrm{60}\right] \\ $$$$=\mathrm{15}×\mathrm{45}=\mathrm{675} \\ $$