Question

Hi !Here is my first tutorial on logarithms ;)

Answer 1

*Logarithms:-
let a & n be positive real numbers such that a is not equal to 1 then\[a^x=N \implies \log_{a}{n}=x \]i.e, log N to the base a.
*Properties of logarithms:-
\[1)\log_{a}{(mn)}=\log_{a}{m}+\log_{a}{n} \]\[2)\log_{a}{\left( m \over n \right)}=\log_{a}{m}-\log_{a}{n} \]\[3)\log_{a}{(m^k)}=k \log_{a}{m} \]\[4)\log_{a}{1}=0 \]\[5)\log_{a}{a}=1 \]* Change of Base:-
\[Let \space \log_{a}{m}=x \space then \space a^x=m\]\[\implies \log_{b}{(a^x)}=\log_{b}{m} \implies x \log_{b}{a}=\log_{b}{m} \]\[(\log_{a}{m} )(\log_{b}{a} )=\log_{b}{m} \space [x=\log_{a}{m} ] \]

Answer 2

\[\log_{a}{m}={[\log_{b}{m}] \over [\log_{b}{a}]} \]

Answer 3

Hi artist @mukushla how is this ;)

Answer 4

Very Useful Tutorial...

Answer 5

Thanx @mukushla

Answer 6

\[\Huge{\color{gold}{\star \star}\color{blue}{\cal{Keep \space It \space Up }}}\]

Answer 7

How do you make the symbols and type in a different font?

Answer 8

me??

Answer 9

Yes

Answer 10

http://openstudy.com/study?login#/groups/LaTeX%20Practicing!%20%3A%29
read here :)

Answer 11

Oh, it's just LaTeX...thought it was an OpenStudy feature, haha

Answer 12

LOL

Answer 13

wonderful start :D but since it's your first time here's some creative criticism ;)

"Try to explain the properties more, and give numerical examples if possible. Also, if you can, prove the definitions"

now it's up to you whether what you do with that advice ^_^

Answer 14

Deserve a medal bro
btw @lgbasallote has a good advice too for u.
just liked that:D

Answer 15

@ajprincess @lalaly @KingGeorge :)

Answer 16

Perfect:D

Answer 17

Really useful one.:)

Answer 18

thanx @lalaly @ajprincess :)

Answer 19

yw.:)

Answer 20

Very informative and something I needed.

Answer 21

Thanx @radar

Answer 22

@satellite73 @amistre64 @waterineyes @mathslover :)

Answer 23

@apoorvk @Diyadiya :)

Answer 24

@phi

Answer 25

@robtobey @Callisto @UnkleRhaukus :)

Answer 26

\[1)\log_{a}{(mn)}=\log_{a}{m}+\log_{a}{n};\qquad a^m\times a^n= a^{m+n}\]
\[2)\log_{a}{\left( m \over n \right)}=\log_{a}{m}-\log_{a}{n};\qquad \frac{a^{m}}{a^n}=a^{m-n}\]
\[3)\log_{a}{(m^k)}=k \log_{a}{m};\qquad\qquad (a^m)^k=a^{mk}\]

Answer 27

@_sam @quarkine @zepp :)

Answer 28

thanx @UnkleRhaukus :)

Answer 29

you see what rules 4) 5) mean for index notation too,
what does the change of base formula look like in index notation?

Answer 30

\[4)\log_{a}{1}=0;\qquad a^0=1\] \[5)\log_{a}{a}=1;\qquad a^1=a\]

Answer 31

thanx a lot @UnkleRhaukus sir!

Answer 32

\[\log_{a}{ab}=\log_{a}{a+b} \]\[\implies ab=a+b\]\[ab-a=b\]\[a(b-1)=b\]\[a= \frac{b}{b-1}\]

Answer 33

thanx for correction @lgbasallote :)

Answer 34

very good tutorial @jiteshmeghwal9 keep it up dude

Answer 35

thanx for the comment:)

Answer 36

u deserved it dude

Answer 37

thanx @mathslover :)

Answer 38

@myininaya @Hero @Ishaan94 @waterineyes have a look:)

Answer 39

A video tutorial on logs would be a great upgrade from this. Imagine a Tutorial section where one could just post math tutorials. It would be much more effective.

Answer 40

\[\LARGE{\color{red}{yes \space !}}\]

Answer 41

lol

Answer 42

\[\LARGE{\color{green}{LOL}}\]

Answer 43

@nbouscal :)

Answer 44

@jiteshmeghwal9 thanks bro

Answer 45

it's my pleasure :)

Answer 46

[; \huge\text{\color{green}{LAUGHING OUT LOUD}} ;]

Answer 47

@him1618 :)

Answer 48

Did mine print out?

Answer 49

i don't get wht u mean to say @Hero

Answer 50

LOL

Answer 51

I'm wondering if people who don't have the chrome tex extension can still see my green print out

Answer 52

If you don't have the chrome tex extension, raise your hand.

Answer 53

i have it

Answer 54

\[[; \huge\text{\color{green}{LAUGHING OUT LOUD}} ;]\]

Answer 55

But it didn't color green :P

Answer 56

ya!

Answer 57

I just wanted to know which one you were using @jitteshmeghwal9 , I just answered my own question.

Answer 58

LARGE{color{green}{Lol}}

Answer 59

@jiteshmeghwal9 doesn't have Chrome TeX

Answer 60

no

Answer 61

i don't have too

Answer 62

@eliassaab @ganeshie8 @.Sam. @AccessDenied :)

Answer 63

I'd like to see some proofs of this identities.

Answer 64

\[\log_{a}{a}=1 \]after changing it into exponential form it will be\[a^1=a\] so it's right that \[\log_{a}{a}=1 \]

Answer 65

Prove the first property please:
\(\log_{a}{(mn)}=\log_{a}{m}+\log_{a}{n}\)

Answer 66

as in exponents \[a^x+a^b=a^{xb}\]similarly is the case with logarithms.

Answer 67

if the bases are same then the powers also should multiplied:)

Answer 68

@klimenkov do u understood???

Answer 69

I think about it now. Wait.

Answer 70

I think that the main property of logarithm is \[a^{\log_a b}=b\]Others can be got from here and from power properties.

Answer 71

i haven't studied about this property:)

Answer 72

I think you will easy understand it. It comes from the definition of the logarithm.