hba
Logarithm-a log sheet to help you guys.
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hba
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\[\Huge{\bf{Law\ of\ Logaritm:}}\]
\[1.\log _{_{a}}a(xy)=\log _{_{a}}x+\log _{a}y\]\[2.\log_a \ (\frac{ x }{ y })=\log_ax-\log_ay\]\[3.\log_ax^m=mlog_ax\]
hba
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\[\Huge{\bf{CHANGE\ OF \ BASE \ OF \ LOG:}}\]
\[\log_aN=\frac{ \log_mN }{ \log_ma }\]
hba
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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,\[e^{lnn}=n\]\[6.\log_ab=\frac{ 1 }{ \log _{a}^{b} } or\ \log_ab*\log_ba=1\]
hba
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@ash2326 @Agent_Sniffles @AccessDenied @cwrw238 @ganeshie8 @him1618 @mayankdevnani @nitz @nubeer @Skaematik @Spectrum
mayankdevnani
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\[\Huge{\color{red}{thnx...} \space \color{blue}{@hba!!!}}\] \[\Huge{\color{green}{\ddot \smile}} \]
mayankdevnani
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\[\huge{\color{red}{\frak{ \space \text{great} \space tutorial \space}\mathbb{Thanx !!!!!!}}}\]
nitz
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good job!
hba
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Thanks a lot guys.
mayankdevnani
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welcome!!
Spectrum
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@hba why didy ou do this ..i have a headache now ._. :3
hba
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@Spectrum I am sorry but i tried my best to simplify it.
Spectrum
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haha im kidding man :3.gj medal for you
hba
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Thanks a lot.
shubhamsrg
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log 0 = infinity ??maybe you mean -infinity..
anyways, i'd say that's neither..its undefined..
hba
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no, log_{a}0 =infty
shubhamsrg
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any valid reason ?
hba
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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.
shubhamsrg
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hmm..
hartnn
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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.
shubhamsrg
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he wrote my mind down! :P
shubhamsrg
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i mean you*`
hartnn
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you realize, u have a typo in 1. @hba
hartnn
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an extra a.
hba
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Oh man,how can i make mistakes :(
hba
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@hartnn Thanks for the feedback though.
hartnn
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i tried to message you, but u won't accept....
hba
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@hartnn Don't worry i am going to make a correction slot.
hba
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\[\Huge{\bf{CORRECTIONS:}}\]
The first law of log
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\[1.\log _{_{a}}(xy)=\log _{_{a}}x+\log _{a}y\]
The useful result area
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\[3.\log_a0= Undefined\]
hba
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@hartnn What say ?
hartnn
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i say 'Good Work' :)
hba
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Thanks :)
hba
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@lalaly
hba
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\[\frak\color{red}{oh\ oooooooooooo}\]
hba
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@hartnn Do you know something which everyone is looking for because i want to make more tutorials ?
hartnn
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if i would've known, i would've made tutorial :P