Welcome to the official YouTube channel of
Mathematics & Beyond.
I am your host sv7 and
today we are going to study
LOGARITHMS
("ta-da")
I know many of you might have read this chapter
or wanted to learn this concept
so we are here to teach u this concept
we will do a full-course on logarithms, many
videos are going to be uploaded to explain
this concept
and now let us start:
"What is/are Logarithms?"
Logarithms is simply another way of thinking
about our friend Exponents which is used almost
every field of mathematics(VERY important)
You should recall that we had learned exponents(indices
in earlier classes, their properties, questions,
etc. because they are very important from
this chapter's point of view.
let us do a very basic property of exponents
before entering the chapter
"what is/are Exponents?"
Exponents is 
a quantity representing the power to which
the number is to be raised or simply the number
of times it is to be multiplied
for ex:- 3^2 = 3x3 this 3^2 is read as 3 squared
2^5 = 2x2x2x2x2 which is 2 multiplied by itself
5 times
in general, exponents are written as " x^n
"(x to the power n), where x is any number
and n is the power(no. of times x is multiplied
by itself)
I hope you have understood exponents, now
let us jump back to our real topic
do you remember -ve exponents(x^-n)
most of u might have had this problem of solving
questions related to them in earlier classes
in ur textbooks and ur, the teacher must have
told you that
x^-n = 1/x^n this is the identity of -ve exponents
why this happens let us have a brief proof(intuition)
let us check it out I have 2 intuitions:
1st :
consider n and x=2 hee
we 
have n=3,2,1,0,-1,-2 2^3=8,2^2=4,2^1=2,2^0=1
,2^-1=1/2 , 2^-2=1/4
so we can see that pattern of division by
2 is formed
on generalizing we get the identity
2nd;
I consider a problem: 2^2/2^3
(easily explained in the video no subtitle
req.)
this was second proof,
now let us jump into logarithms
why log is useful
if I ask u what is x if 2^x=2^3 u will spontaneously
reply 3
if I ask u what is x if x^3=2^3 u will spontaneously
reply 2
if I ask u what is x if 3^x=5^2
I hope(wrong word use: feel is correct) that
many of u might not answer this question spontaneously
but u can answer if u have read this chapter
or any trick
for such
problems and 
other day to day life applications, this concept
is used.
will
discuss them
in upcoming videos
that is
all for today.
in the next lecture, we continue this chapter
it is time for the question of 
the day:
e-mail the answer by going to the website:
http://07052003-2203.renderforestsites.com/
and win a chance to get ur name featured on
my board.
check out the question on our website if not
readable.
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