მათემატიკა

c

gavalogariTmoT igiveoba

fuZiT

ZiriTadi

logariTmuli

a log a b = b .

gveqneba

(

)

log c a log a b = log c b .

aqedan

log a b ⋅ log c a = log c b ,

saidanac log c b . log c a Tu (1) formulaSi c –s SevcvliT b –Ti, miviRebT 1 . log a b = log b a log a b =

Tu miRebul gveqneba:

formulaSi

log a k b =

a –s

SevcvliT

a k –Ti,

1 1 1 = = log a b . log b a k k log b a k

amrigad log a k b =

1 log a b , (b > 0, k ≠ 0 ) . k

§74. mphbsjUnvmj!gvordjjt!Uwjtfcfcj!eb!hsbgjlj!

! vinaidan

y=a

x

funqcia

(a > 0,

a ≠ 1)

amitom mas gaaCnia Seqceuli funqcia.

y=a

monotonuria, x

tolobidan

x = log a y . Tu am tolobaSi cvladebs gansazRvrebiT gadavanacvlebT, miviRebT y = log a x , romelic warmoadgens y = a x funqciis Seqceul funqcias. (a > 0, a ≠ 1) , logariTmuli y = log a x saxis funqcias funqcia ewodeba. radgan logariTmuli funqcia warmoadgens maCvenebliani funqciis Seqceul funqcias,

amitom y = log a x funqciis grafiki simetriulia y = a x funqciis grafikisa y = x wrfis mimarT (nax. 81, 82). maCvenebliani funqciis Tvisebebidan gamomdinareobs misi Seqceuli logariTmuli funqciis Tvisebebi: 150