logarytmy Ireneusz: Oblicz log₂360 wiedząc, że log₂20=a a log₂15=b

Jack: podpowiedź : 360 = 20 * 15 + 4 * 15

Jack: albo nie... wlasciwie

Jack: log₂20 = log₂(4*5) = log₂4 + log₂5 = 2 + log₂5 = a ===>> log₂5 = a − 2 log₂15 = log₂ (3*5) = log₂3 + log₂5 = b ===> log₂5 = b − log₂3 a − 2 = b − log₂3 log₂3 = b − a + 2 log₂360 = log₂(24 * 15) = log₂ 24 + log₂15 = = log₂(8*3) + b = log₂8 + log₂3 + b = 3 + b + log₂3 = = 3 + b + b − a + 2 = 5 + 2b − a

Eta: log₂20=a ⇒ 2+log₂5=a ⇒ log₂5=a−2 log₂15= log₂3+log₂5=b ⇒ log₂3=b−a+2 log₂360= log₂3²*20*2= 2log₂3+log₂20+1 = 2(b−a+2)+a+1= 2b−a+5