Funktjuun faan a 10er logarithmus Di tjiiner logarithmus as di logarithmus mä det grünjtaal 10. Hi woort so apskrewen:
lg
x
{\displaystyle \lg x}
log
10
x
.
{\displaystyle \log _{10}x\,.}
Sin kiarfunktjuun as
10
x
{\displaystyle 10^{x}}
y
=
10
x
{\displaystyle y=10^{x}}
x
=
lg
y
.
{\displaystyle x=\lg y\,.}
Hi het tjiiner logarithmus, auer dü uk logarithmen mä ööder grünjtaalen bereegne könst. Jo haa oober ei son grat bedüüdang.
Iar skrääpreegnern apkaam, skul am a logarithmen faan logarithmentoofeln uflees. Diar wiar oober bluas a logarithmen faan a taalen 1 bit 10 uun. Wan dü nü di logarithmus faan 120 wed wulst, skulst dü efterluke:
log
10
1
,
2
≈
0,079
18
{\displaystyle \log _{10}1{,}2\approx 0{,}07918}
an do reegne:
log
10
120
=
log
10
(
10
2
⋅
1
,
2
)
=
2
+
log
10
1
,
2
≈
2,079
18
{\displaystyle \log _{10}120=\log _{10}(10^{2}\cdot 1{,}2)=2+\log _{10}1{,}2\approx 2{,}07918}
Dü wel wed, hüfölsis dü det taal 7 mä ham salew moolnem skel, amdat 16807 ütjkomt:
7
x
=
16807
{\displaystyle 7^{x}=16807}
Do reegenst dü
x
⋅
lg
7
=
lg
16807
{\displaystyle x\cdot \lg 7=\lg 16807}
An do dialst dü
x
=
lg
16807
:
lg
7
{\displaystyle x=\lg 16807:\lg 7}
x
=
4
,
225...
:
0
,
845...
{\displaystyle x=4,225...:0,845...}
x
=
5
{\displaystyle x=5}
Det ment:
7
5
=
16807
{\displaystyle 7^{5}=16807}
An auer di logarithmus en stüdag funksion as, säär för
x
{\displaystyle x}
natüürelk taal ütjkem:
7
x
=
20000
{\displaystyle 7^{x}=20000}
x
⋅
lg
7
=
lg
20000
{\displaystyle x\cdot \lg 7=\lg 20000}
x
=
lg
20000
:
lg
7
{\displaystyle x=\lg 20000:\lg 7}
x
=
4
,
301...
:
0
,
845...
{\displaystyle x=4,301...:0,845...}
x
=
5
,
089...
{\displaystyle x=5,089...}
Det ment:
7
5
,
089
≈
20000
{\displaystyle 7^{5,089}\approx 20000}
Tekst üüb Öömrang
