Logaritma (Logarithm ) ebe menay luğati ra çarpkerdış u barkerdışê gırdi, seba kok u quwet gırotış kerdene yew raya matematikio. Mısal; gorey tebano 10ın ra logaritmaya 1000 3 o. Çunki 1000 quwetê desio hirıno, yani 1000 = 10 × 10 × 10 = 103. Şekılê logaritmay ewroyên sesera 18ıne de terefê matematikşinaso İswiçreyıc Leonhard Euler ra keşf biyo. İşaretê logaritma
log
a
b
{\displaystyle \log _{a}b\,}
Grafikê logaritma Ebe ifadey pêroyi :
x
=
b
y
⇔
log
b
(
x
)
=
y
{\displaystyle x=b^{y}\Leftrightarrow \log _{b}(x)=y}
log
b
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x
y
)
=
log
b
(
x
)
+
log
b
(
y
)
.
{\displaystyle \log _{b}(xy)=\log _{b}(x)+\log _{b}(y).\,}
Eke teban deso, logaritmaya desıni ya zi logaritmaya pêroyi vaciyeno. Fen u muhendisiye de cay logaritma zafo.
bıvurne
Hısusiyet
Mısal
Çarpkerdış
log
b
(
x
y
)
=
log
b
(
x
)
+
log
b
(
y
)
{\displaystyle \log _{b}(xy)=\log _{b}(x)+\log _{b}(y)\,}
log
3
(
243
)
=
log
3
(
9
⋅
27
)
=
log
3
(
9
)
+
log
3
(
27
)
=
2
+
3
=
5
{\displaystyle \log _{3}(243)=\log _{3}(9\cdot 27)=\log _{3}(9)+\log _{3}(27)=2+3=5\,}
Barekerdış
log
b
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x
y
)
=
log
b
(
x
)
−
log
b
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y
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{\displaystyle \log _{b}\!\left({\frac {x}{y}}\right)=\log _{b}(x)-\log _{b}(y)\,}
log
2
(
16
)
=
log
2
(
64
4
)
=
log
2
(
64
)
−
log
2
(
4
)
=
6
−
2
=
4
{\displaystyle \log _{2}(16)=\log _{2}\!\left({\frac {64}{4}}\right)=\log _{2}(64)-\log _{2}(4)=6-2=4}
Üs
log
b
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x
p
)
=
p
log
b
(
x
)
{\displaystyle \log _{b}(x^{p})=p\log _{b}(x)\,}
log
2
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64
)
=
log
2
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2
6
)
=
6
log
2
(
2
)
=
6
{\displaystyle \log _{2}(64)=\log _{2}(2^{6})=6\log _{2}(2)=6\,}
Rıstım
log
b
x
p
=
log
b
(
x
)
p
{\displaystyle \log _{b}{\sqrt[{p}]{x}}={\frac {\log _{b}(x)}{p}}\,}
log
10
1000
=
1
2
log
10
1000
=
3
2
=
1.5
{\displaystyle \log _{10}{\sqrt {1000}}={\frac {1}{2}}\log _{10}1000={\frac {3}{2}}=1.5}
log
b
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x
)
=
log
k
(
x
)
log
k
(
b
)
.
{\displaystyle \log _{b}(x)={\frac {\log _{k}(x)}{\log _{k}(b)}}.\,}
log
b
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x
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=
log
10
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x
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log
10
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b
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=
log
e
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x
)
log
e
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b
)
.
{\displaystyle \log _{b}(x)={\frac {\log _{10}(x)}{\log _{10}(b)}}={\frac {\log _{e}(x)}{\log _{e}(b)}}.\,}
Pêro de hiri tebanê logaritma esto ;
Teban
Namelogb x )
Asayışo ISO
Asayışê bini
Kamci ca de kullanbeno
2
Logaritmaya dıyıni
lb(x )
ld(x ), log(x ), lg(x ), log2(x )
komputeriye ,teoriya melumati, matematik, teoriya muzigi
e
Logaritmaya tebii
ln(x )
matematik, fizik, kimya,
10
Logaritmaya adi
lg(x )
log(x )x )
![{\displaystyle \log _{b}{\sqrt[{p}]{x}}={\frac {\log _{b}(x)}{p}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca0e5324b82de66458079f9ed2b47bad05a6abbe)
