Assalamualaikum warahmatullahi wabarakatuh
Welcome to subtopic 1.3.
Logarithm.
I know some of you are afraid of the name but don't be. We'll go through this
together step by step.
So by the end of this subtopic you
should be able to define and state the
laws of logarithm, change the base of
logarithm and last but not least to solve
equations involving logarithm.
Let's begin with its definition.
There is more formal way to define log,
but generally log is the reverse process
of index. Just like the relation between
addition with subtraction, multiplication
with division and so on
We've seen index in our very first video
in a^y where a is the base and y is
the power let's say this is equal to x.
If I want to find y I can move a to
the other side and this will become log
like this. y equals to log of x base a.
This is called the index form and this
is called the log form. a is still called
the base in both form.
Let's test you say we have 3^y =x.
This is an index form with 3 as the base.
Let's find y. We are going to move this base here to the other side and
make it as log form.
So this will become
y=log(x) base 3
Once more and then
we'll move on. Try to change to
2^a =b into a log form.
Can you do it?
Is a=log(b) base 2 your answer?
Very good.
Now we can move on there are two special
bases in logarithm base 10 and base e.
Normally any base would be written like
this and the correct way to say this is
log(b) base a
we always say the number first
then the base, for example, this
this is not log 2 4, that's wrong.
This is log(4) base 2.
Let's see base 10 over here.
As you can see here.
This is log(b) base 10. For this one.
We can just write this as log(b)..
If a log doesn't have any base written
here, that means it belongs to base 10
and we can just say it as log(b).
For example log(4) this one belongs to base 10.
You don't have to write base 10 to know
that it belongs to base 10
and finally log with base e.
e is a number with value 2.718
and so on.
This is called Euler number.
like \pi which is 3.14 2 and so on
any log with base e can be written as ln.
log(b) base e can be written as just ln(b).
that is small letter l with small letter n.
For example if we have log(3) base e.
Write this as ln(3).
Very well, so we'll continue with laws of log in the next video.
Thank you for your attention and have a
great day.
Take care.
