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  • hba

Logarithm-a log sheet to help you guys.

Mathematics
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  • hba
\[\Huge{\bf{Law\ of\ Logaritm:}}\] \[1.\log _{_{a}}a(xy)=\log _{_{a}}x+\log _{a}y\]\[2.\log_a \ (\frac{ x }{ y })=\log_ax-\log_ay\]\[3.\log_ax^m=mlog_ax\]
  • hba
\[\Huge{\bf{CHANGE\ OF \ BASE \ OF \ LOG:}}\] \[\log_aN=\frac{ \log_mN }{ \log_ma }\]
  • 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,\[e^{lnn}=n\]\[6.\log_ab=\frac{ 1 }{ \log _{a}^{b} } or\ \log_ab*\log_ba=1\]

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\[\Huge{\color{red}{thnx...} \space \color{blue}{@hba!!!}}\] \[\Huge{\color{green}{\ddot \smile}} \]
\[\huge{\color{red}{\frak{ \space \text{great} \space tutorial \space}\mathbb{Thanx !!!!!!}}}\]
good job!
  • hba
Thanks a lot guys.
welcome!!
@hba why didy ou do this ..i have a headache now ._. :3
  • hba
@Spectrum I am sorry but i tried my best to simplify it.
haha im kidding man :3.gj medal for you
  • hba
Thanks a lot.
log 0 = infinity ??maybe you mean -infinity.. anyways, i'd say that's neither..its undefined..
  • hba
no, log_{a}0 =infty
any valid reason ?
  • 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.
hmm..
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.
he wrote my mind down! :P
i mean you*`
you realize, u have a typo in 1. @hba
an extra a.
  • hba
Oh man,how can i make mistakes :(
  • hba
@hartnn Thanks for the feedback though.
i tried to message you, but u won't accept....
  • hba
@hartnn Don't worry i am going to make a correction slot.
  • hba
\[\Huge{\bf{CORRECTIONS:}}\] The first law of log --------------- \[1.\log _{_{a}}(xy)=\log _{_{a}}x+\log _{a}y\] The useful result area ------------------ \[3.\log_a0= Undefined\]
  • hba
@hartnn What say ?
i say 'Good Work' :)
  • hba
Thanks :)
  • hba
  • hba
\[\frak\color{red}{oh\ oooooooooooo}\]
  • hba
@hartnn Do you know something which everyone is looking for because i want to make more tutorials ?
if i would've known, i would've made tutorial :P

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