Qeexida logarithm-ka, sifooyinka iyo garaafyada

Logarithm ee nambarka waa awooda ay tahay in hal tiro kor loo qaado si loo helo mid kale.

Haddii lambarka b ilaa xad y isku mid ah x:

b^y = x

Sidaas logarithm ee tirada x sabab ahaan b is y:

y = diiwaan_b(X)

Tusaale ahaan:

2⁴ = 16

gasho₂(16) = 4

Logarithm-ku wuxuu u shaqeeyaa beddelka jibbaarada

shaqada logarithmic y = diiwaan_b(x) waa shaqada rogan ee jibbaarada x=b ^y.

Markaa haddii aan xisaabino shaqada jibbaarada ee logarithm-ka x (x > 0), waxay noqon doontaa:

f (f ^-1(x)) = b^gashob^(x) = x

Ama haddii aan xisaabinno logarithm-ka shaqada jibbaarada х:

f ^-1(f (x)) = log_b(b^x) = x

Logarithm-ka dabiiciga ah (ln)

Logarithm-ka dabiiciga ah waa logarithm-ka aasaasiga ah е.

ln (x) = log_e(x)

Number e waa mid joogto ah oo lagu qeexi karo xad:

Ama sidaas:

Logarithm-ka rogan

Logarithm rogaal celis ah (ama antilogarithm) ee lambar n waa tiro saldhigiisu yahay logarithm a waxay le'eg tahay tirada n.

geed qudhaanjada_an = aⁿ

Shaxda guryaha ee logarithms

Hoos waxaa ku yaal sifooyinka ugu muhiimsan ee logarithms ee qaabka shaxda.