Question Number 197312 by mathlove last updated on 13/Sep/23
$$\frac{\left({log}_{\mathrm{2}} \mathrm{20}\right)^{\mathrm{2}} −\left({log}_{\mathrm{2}} \mathrm{5}\right)^{\mathrm{2}} }{{log}_{\mathrm{2}} \mathrm{10}}=? \\ $$
Answered by som(math1967) last updated on 13/Sep/23
$$\mathrm{4} \\ $$
Commented by som(math1967) last updated on 13/Sep/23
$$\:\frac{\left({log}_{\mathrm{2}} \mathrm{20}+{log}_{\mathrm{2}} \mathrm{5}\right)\left({log}_{\mathrm{2}} \mathrm{20}−{log}_{\mathrm{2}} \mathrm{5}\right)}{{log}_{\mathrm{2}} \mathrm{10}} \\ $$$$=\frac{{log}_{\mathrm{2}} \mathrm{100}×{log}_{\mathrm{2}} \mathrm{4}}{{log}_{\mathrm{2}} \mathrm{10}} \\ $$$$=\frac{\mathrm{2}{log}_{\mathrm{2}} \mathrm{10}×\mathrm{2}{log}_{\mathrm{2}} \mathrm{2}}{{log}_{\mathrm{2}} \mathrm{10}} \\ $$$$=\mathrm{4} \\ $$