Question Number 227880 by hardmath last updated on 23/Feb/26
$$\mathrm{Find}:\:\:\:\frac{\mathrm{log}_{\mathrm{2}} ^{\mathrm{2}} \:\mathrm{20}\:−\:\mathrm{log}_{\mathrm{2}} ^{\mathrm{2}} \:\mathrm{5}}{\mathrm{log}_{\mathrm{2}} \mathrm{10}}\:=\:? \\ $$
Answered by efronzo1 last updated on 23/Feb/26
$$\:=\:\frac{\left(\mathrm{log}_{\mathrm{2}} \left(\:\mathrm{20}×\mathrm{5}\right)\right)\left(\mathrm{log}_{\mathrm{2}} \left(\:\frac{\mathrm{20}}{\mathrm{5}}\right)\right)}{\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{10}\right)} \\ $$$$\:=\:\frac{\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{4}\right)×\mathrm{2log}\:_{\mathrm{2}} \left(\mathrm{10}\right)}{\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{10}\right)}\:=\:\mathrm{4} \\ $$