Question

Logarithm-a log sheet to help you guys.

Answer 1

\[\Huge{\bf{Law\ of\ Logaritm:}}\]

\[1.\log _{_{a}}a(xy)=\log _{_{a}}x+\log _{a}y\]\[2.\log_a \ (\frac{ x }{ y })=\log_ax-\log_ay\]\[3.\log_ax^m=mlog_ax\]

Answer 2

\[\Huge{\bf{CHANGE\ OF \ BASE \ OF \ LOG:}}\]

\[\log_aN=\frac{ \log_mN }{ \log_ma }\]

Answer 3

\[\Huge{\bf{SOME\ USEFUL\ RESULTS:}}\]

\[1.\log_aa=1\]\[2.\log_a1=0\]\[3.\log_a0=\infty \]\[4.\log_ab*\log_ca=\log_cb\]\[5.a^{\log_a^n}=n\]In particular,\[e^{lnn}=n\]\[6.\log_ab=\frac{ 1 }{ \log _{a}^{b} } or\ \log_ab*\log_ba=1\]

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

good job!

Answer 8

Thanks a lot guys.

Answer 9

welcome!!

Answer 10

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

Answer 11

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

Answer 12

haha im kidding man :3.gj medal for you

Answer 13

Thanks a lot.

Answer 14

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

Answer 15

no, log_{a}0 =infty

Answer 16

any valid reason ?

Answer 17

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.

Answer 18

hmm..

Answer 19

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.

Answer 20

he wrote my mind down! :P

Answer 21

i mean you*`

Answer 22

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

Answer 23

an extra a.

Answer 24

Oh man,how can i make mistakes :(

Answer 25

@hartnn Thanks for the feedback though.

Answer 26

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

Answer 27

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

Answer 28

\[\Huge{\bf{CORRECTIONS:}}\]

The first law of log
---------------

\[1.\log _{_{a}}(xy)=\log _{_{a}}x+\log _{a}y\]


The useful result area
------------------

\[3.\log_a0= Undefined\]

Answer 29

@hartnn What say ?

Answer 30

i say 'Good Work' :)

Answer 31

Thanks :)

Answer 32

@lalaly

Answer 33

\[\frak\color{red}{oh\ oooooooooooo}\]

Answer 34

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

Answer 35

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