Question

Tutorial:
Basic Logarithmic Rules

Answer 1

\[\Large1)\ If\ \ a^x=b\ then -->\log_{a} b=x\]

Answer 2

\[\Large\ 2)\ \log_{a} (m.n)=\log_{a}m+\log_{a}n\]

Answer 3

\[\Large\ 3)\log_{a} (m/n)=\log_a{m}-\log_{a}n\]

Answer 4

\(\Large\ 4)\color{green}{Change\ Of\ Base:} \)
\[\Large\ A.\log_{a}b=\log_{m}b/\log_{m}a\ (a,b,m>0\ a \neq1)\]
\[\Large\ B.\log_{a}b=1/\log_{b}a\ \Large\ OR\ \log_{a}b\ .\ \log_{b}a=1\]

Answer 5

\(\Large\ 5)\color{gold}{The\ Golden\ Rules :}\)
\[\Large\color{gold} {A.}\ \color{goldenrod}{\log_{a}1=0\ where\ a>0\ ,\ a \neq1 } \]
\[\Large\color{gold} {B.}\ \color{goldenrod}{\log_a{a}=1\ where\ a>0\ ,\ a \neq1}\]
\[\Large\color{gold} {C.}\ \color{goldenrod}{a^{\log_{a}x}=x\ where\ a>0\ ,\ a \neq1 }\]
\[\Large\color{gold} {D.}\ \color{goldenrod}{\log_{a}m^n=n .\log_{a}m\ where\ m,a>0\ ,\ a \neq1}\]

Answer 6

good job!

Answer 7

I didn't understand number 2
can anyone give some examples?

Answer 8

okay
\[\log_{a}(15\ X\ 5)= \log_{a}15+\log_{a}5\]

Answer 9

I see
the little a is what I should be considering as the base?

Answer 10

yeah a is the base here

Answer 11

I see..

so are there cases where (as you said in rule 2) where we have to find out the base?
in cases like that, how do we find the base? :o

Answer 12

normally the base is e in calculus
and 10 in other cases
Also the base is mentioned if it is not 10 or e

Answer 13

Oh okay, so can I consider e as constant in calculus? (like I would with Pi ?)

Answer 14

yeah
its value is : e=2.71828

Answer 15

thanks rvc!
good job on the tutorial
I'm just starting out logarithm so, this is gonna be pretty uselful

Answer 16

Yeah
Thank you
Hope this helps you @nopen :)

Answer 17

Nice one @rvc

Answer 18

I don't know any of this ..but I will come to you rennyz ^.^

Answer 19

thanks

Answer 20

And I give you medal