Question Number 25113 by Mr easy last updated on 04/Dec/17
Commented by prakash jain last updated on 05/Dec/17
![(log_2 x)^3 +(log_2 y)^3 =(log_2 x+log_2 y)[(log_2 x)^2 +(log_2 y)^2 −(log_2 x)(log_2 y)] =(log_2 xy)[(log_2 x+log_2 y)^2 −3(log_2 x)(log_2 y)] =(log_2 xy)[(log_2 xy)^2 −3(log_2 x)(log_2 y)] =15[15^2 −3×60] =15×45=675](https://www.tinkutara.com/question/Q25147.png)
$$\left(\mathrm{log}_{\mathrm{2}} {x}\right)^{\mathrm{3}} +\left(\mathrm{log}_{\mathrm{2}} {y}\right)^{\mathrm{3}} \\ $$$$=\left(\mathrm{log}_{\mathrm{2}} {x}+\mathrm{log}_{\mathrm{2}} {y}\right)\left[\left(\mathrm{log}_{\mathrm{2}} {x}\right)^{\mathrm{2}} +\left(\mathrm{log}_{\mathrm{2}} {y}\right)^{\mathrm{2}} −\left(\mathrm{log}_{\mathrm{2}} {x}\right)\left(\mathrm{log}_{\mathrm{2}} {y}\right)\right] \\ $$$$=\left(\mathrm{log}_{\mathrm{2}} {xy}\right)\left[\left(\mathrm{log}_{\mathrm{2}} {x}+\mathrm{log}_{\mathrm{2}} {y}\right)^{\mathrm{2}} −\mathrm{3}\left(\mathrm{log}_{\mathrm{2}} {x}\right)\left(\mathrm{log}_{\mathrm{2}} {y}\right)\right] \\ $$$$=\left(\mathrm{log}_{\mathrm{2}} {xy}\right)\left[\left(\mathrm{log}_{\mathrm{2}} {xy}\right)^{\mathrm{2}} −\mathrm{3}\left(\mathrm{log}_{\mathrm{2}} {x}\right)\left(\mathrm{log}_{\mathrm{2}} {y}\right)\right] \\ $$$$=\mathrm{15}\left[\mathrm{15}^{\mathrm{2}} −\mathrm{3}×\mathrm{60}\right] \\ $$$$=\mathrm{15}×\mathrm{45}=\mathrm{675} \\ $$