## hba 2 years ago Logarithm-a log sheet to help you guys.

1. hba

$\Huge{\bf{Law\ of\ Logaritm:}}$ $1.\log _{_{a}}a(xy)=\log _{_{a}}x+\log _{a}y$$2.\log_a \ (\frac{ x }{ y })=\log_ax-\log_ay$$3.\log_ax^m=mlog_ax$

2. hba

$\Huge{\bf{CHANGE\ OF \ BASE \ OF \ LOG:}}$ $\log_aN=\frac{ \log_mN }{ \log_ma }$

3. hba

$\Huge{\bf{SOME\ USEFUL\ RESULTS:}}$ $1.\log_aa=1$$2.\log_a1=0$$3.\log_a0=\infty$$4.\log_ab*\log_ca=\log_cb$$5.a^{\log_a^n}=n$In particular,$e^{lnn}=n$$6.\log_ab=\frac{ 1 }{ \log _{a}^{b} } or\ \log_ab*\log_ba=1$

4. hba

@ash2326 @Agent_Sniffles @AccessDenied @cwrw238 @ganeshie8 @him1618 @mayankdevnani @nitz @nubeer @Skaematik @Spectrum

5. mayankdevnani

$\Huge{\color{red}{thnx...} \space \color{blue}{@hba!!!}}$ $\Huge{\color{green}{\ddot \smile}}$

6. mayankdevnani

$\huge{\color{red}{\frak{ \space \text{great} \space tutorial \space}\mathbb{Thanx !!!!!!}}}$

7. nitz

good job!

8. hba

Thanks a lot guys.

9. mayankdevnani

welcome!!

10. Spectrum

@hba why didy ou do this ..i have a headache now ._. :3

11. hba

@Spectrum I am sorry but i tried my best to simplify it.

12. Spectrum

haha im kidding man :3.gj medal for you

13. hba

Thanks a lot.

14. shubhamsrg

log 0 = infinity ??maybe you mean -infinity.. anyways, i'd say that's neither..its undefined..

15. hba

no, log_{a}0 =infty

16. shubhamsrg

any valid reason ?

17. hba

I know i have read this and it can be either + infty or - infty so as we are not sure,I may go with Undefined,Thanks for the feedback.

18. shubhamsrg

hmm..

19. hartnn

log 0 is undefined but if we have to choose from +inf and -inf, it would definitely be -inf. a^inf =0 doesn't make sense, inf is very large number, a^inf also is. a^-inf =0 makes sense, more appropriately, its very very small number tending to 0.

20. shubhamsrg

he wrote my mind down! :P

21. shubhamsrg

i mean you*`

22. hartnn

you realize, u have a typo in 1. @hba

23. hartnn

an extra a.

24. hba

Oh man,how can i make mistakes :(

25. hba

@hartnn Thanks for the feedback though.

26. hartnn

i tried to message you, but u won't accept....

27. hba

@hartnn Don't worry i am going to make a correction slot.

28. hba

$\Huge{\bf{CORRECTIONS:}}$ The first law of log --------------- $1.\log _{_{a}}(xy)=\log _{_{a}}x+\log _{a}y$ The useful result area ------------------ $3.\log_a0= Undefined$

29. hba

@hartnn What say ?

30. hartnn

i say 'Good Work' :)

31. hba

Thanks :)

32. hba

@lalaly

33. hba

$\frak\color{red}{oh\ oooooooooooo}$

34. hba

@hartnn Do you know something which everyone is looking for because i want to make more tutorials ?

35. hartnn

if i would've known, i would've made tutorial :P