Loogarizimii

Kana jechuun lakkoofsa barbaadame argachuuf hundee sana gara aangoo/powarii akkamii ol kaasuu akka qabnu nutti hima. Herregaa keessatti loogaritmiin akka, . ${\displaystyle \log _{a}b}$ tti barreffama yeeroo dubbiisnuu "Loogaritmii x gara Hundee b" fi "lakkoofsi hundee a yoo meeqaan aaangeeffame lakkoofsa b kenna?" Jechuu wajjin tokko. ${\displaystyle \log _{a}b=x\,}$ Ta'e ${\displaystyle a^{x}=b\,\!}$ ta'uu isaati.

fakkeenya:

${\displaystyle \log _{3}9=2\,}$ Yeroo dubbifamu "loogaritmiin 9 gara hundee 3tti 2 ta'a" sababni isaas 3 ² = 9.

Amaloota loogaritmii

Amaloonni armaan gadii kallattiin hiika hundee loogaritmii qabu irraa hordofu

a > 0 fi a ≠ 1 ta’a

a ^c = b → ${\displaystyle {\log _{a}b}=c}$ 

a = Hundee

b = bu’aa

c = aangeessoo ykn ekispoonantii

1. log𝑎 1 = 0 sababnisaa 𝑎0 = 1.
2. log𝑎 𝑎 = 1 sababnisaa 𝑎1 = 𝑎.
3. log𝑎 𝑎𝑝 = 𝑝 fi 𝑎log𝑎 𝑝 = 𝑝 . . . Hariiroo fuggisoo
4. If log𝑎 M = log𝑎 N, then M = N . . . Amala tokko tokkof
5. ${\displaystyle \log _{a}(bc)\ =\log _{a}|b|+\log _{a}|c|\quad (bc>0)}$ 
6. ${\displaystyle \log _{a}{\frac {b}{c}}=\log _{a}|b|-\log _{a}|c|\quad \left({\frac {b}{c}}>0\right)}$ 
7. ${\displaystyle \log _{a}b={\frac {\log _{c}b}{\log _{c}a}}}$ 
8. ${\displaystyle \log _{a}(b^{p})=p\ \log _{a}|b|\quad (b^{p}>0)}$ 
9. ${\displaystyle \log _{a}{\sqrt[{k\,}]{x}}=\log _{a^{k}}b={\frac {1}{k}}\log _{a}b}$ 
10. ${\displaystyle \log _{a}{\sqrt[{k\,}]{x}}=\log _{a^{k}}b={\frac {1}{k}}\log _{a}b}$ 
11. ${\displaystyle a^{log_{c}d}=d^{log_{c}a}}$ 

 

Faankishiniin loogaritmii  "log" kan agarsiifamu yoo ta'u, qaamolee gurguddoo lama qaba: hundee fi raggaasa(argument). Hundeen lakkoofsa pozaatiivii kamiyyuu 1 ol ta’uu danda’a, 1 mataa isaa  malee. Raggaasni lakkoofsa loogaritmii argachuu barbaannudha.