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hba

  • 3 years ago

Logarithm-a log sheet to help you guys.

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

  2. hba
    • 3 years ago
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    \[\Huge{\bf{CHANGE\ OF \ BASE \ OF \ LOG:}}\] \[\log_aN=\frac{ \log_mN }{ \log_ma }\]

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

  4. hba
    • 3 years ago
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    @ash2326 @Agent_Sniffles @AccessDenied @cwrw238 @ganeshie8 @him1618 @mayankdevnani @nitz @nubeer @Skaematik @Spectrum

  5. mayankdevnani
    • 3 years ago
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    \[\Huge{\color{red}{thnx...} \space \color{blue}{@hba!!!}}\] \[\Huge{\color{green}{\ddot \smile}} \]

  6. mayankdevnani
    • 3 years ago
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    \[\huge{\color{red}{\frak{ \space \text{great} \space tutorial \space}\mathbb{Thanx !!!!!!}}}\]

  7. nitz
    • 3 years ago
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    good job!

  8. hba
    • 3 years ago
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    Thanks a lot guys.

  9. mayankdevnani
    • 3 years ago
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    welcome!!

  10. Spectrum
    • 3 years ago
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    @hba why didy ou do this ..i have a headache now ._. :3

  11. hba
    • 3 years ago
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    @Spectrum I am sorry but i tried my best to simplify it.

  12. Spectrum
    • 3 years ago
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    haha im kidding man :3.gj medal for you

  13. hba
    • 3 years ago
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    Thanks a lot.

  14. shubhamsrg
    • 3 years ago
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    log 0 = infinity ??maybe you mean -infinity.. anyways, i'd say that's neither..its undefined..

  15. hba
    • 3 years ago
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    no, log_{a}0 =infty

  16. shubhamsrg
    • 3 years ago
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    any valid reason ?

  17. hba
    • 3 years ago
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    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
    • 3 years ago
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    hmm..

  19. hartnn
    • 3 years ago
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    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
    • 3 years ago
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    he wrote my mind down! :P

  21. shubhamsrg
    • 3 years ago
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    i mean you*`

  22. hartnn
    • 3 years ago
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    you realize, u have a typo in 1. @hba

  23. hartnn
    • 3 years ago
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    an extra a.

  24. hba
    • 3 years ago
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    Oh man,how can i make mistakes :(

  25. hba
    • 3 years ago
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    @hartnn Thanks for the feedback though.

  26. hartnn
    • 3 years ago
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    i tried to message you, but u won't accept....

  27. hba
    • 3 years ago
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    @hartnn Don't worry i am going to make a correction slot.

  28. hba
    • 3 years ago
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    \[\Huge{\bf{CORRECTIONS:}}\] 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
    • 3 years ago
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    @hartnn What say ?

  30. hartnn
    • 3 years ago
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    i say 'Good Work' :)

  31. hba
    • 3 years ago
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    Thanks :)

  32. hba
    • 3 years ago
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    @lalaly

  33. hba
    • 3 years ago
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    \[\frak\color{red}{oh\ oooooooooooo}\]

  34. hba
    • 3 years ago
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    @hartnn Do you know something which everyone is looking for because i want to make more tutorials ?

  35. hartnn
    • 3 years ago
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    if i would've known, i would've made tutorial :P

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