Assalamualaikum warahatullahi wabarakatuh
In this video, we will discuss how to solve equations
involving log and if you remember in
subtopic 1.1 about solving equations
involving indices, I told you about two
cases of them, which I then said that we
will discuss that in chapter 1.3
so we will see that too in this video.
Let's start with equation of log first.
Similarly,
We need to make sure all in the same base.
So we have base 2 and base 4. For this
solution
I choose base 2 so I need to change base 4. So
and because I know 4 can be written as 2^2
and if you remember we can bring forward the power
You have two options to solve this. You
can either make them as one log term or
you could move one log to the other side
and then compare them for this solution.
I'm going to make them as one log term.
So to make them as one log term, I need
to move this one back as its power.
So this one will be
and because this is log - log with
the same base.
I can combine this as division.
So this one will become
after we make them as one log term
We are going to change this into index
form.
Do you still remember how to do this?
If not you can always check back the
video before this.
So this one will become
and you know that 2^0=1
and to solve this we are going to
cross multiply this over here.
So this will become
Now this one becomes equation of surds.
Again.
If you don't remember how to solve this
you could always check the video before this
So the next thing that we're going to do
is square both sides.
This one becomes
So move everything to one side.
So we have x=4 and x=-1, just like in surd you need to
recheck this too but you don't have to
make table for it.
Just make sure that the solution that you
have over here
won't be negative in its original equation .
Now 4 is acceptable because it doesn't
become negative in the original equation.
On the other hand,
We're going to reject -1 because if
we substitute it back into here.
It will become negative.
Therefore our final answer over here
is x=4.
Let's look at the next one. For this one.
I'll show you another method the same as
before always make sure that they are
all in the same base.
All of these are in ln, therefore they
are all belong to base e for this one.
I'll show you another method in our
previous solution.
We use this solution over here.
Now, I'm going to show you how to use
this solution the same as before.
Always make sure they are all in the same base since all of these are in ln therefore
they all belong to base e.
We are going to solve this by comparison
and to do that you need to make sure
that you only have one log term on left
hand side
and you only have one log term
in the right hand side.
Look at this side over here.
We have two log term.
So we need to combine them first. To
combine them we need to bring this back up.
So this will become
and subtraction will become division.
So left hand side will be
Now that we have one log on left hand
side and we have one log on right hand side
Then we can compare this.
So by comparing this will be
We can cross multiply this over there.
So this will become
One and lastly we have x=1/4
Always re-check your answer just
make sure that the solution that we got
doesn't become negative in the original
equation.
If it does you need to reject this. In
this case, we have x=1/4,
if we substitute this back into here and
over here, will it become negative the
answer is NO. Therefore this is our final
answer. Right.
So let's move on to equation of indices
with different bases.
In chapter 1.1, we already discuss
equation of indices with the same base.
To solve equation of indices with
different bases.
We need to add log both sides. See this
one has base 4
and this one has base 5, since they
don't have the same base.
All we need to do is to add log both
sides.
You can decide any base for that log.
It doesn't matter. For this solution.
I choose to have base e.
So I'm going to add ln on both sides,
so this will become
By rules of log.
We can bring forward this power here
as its constant.
We can bring forward this power over here.
Therefore this will become
We can expand this and this will become
So we're going to bring this over here
and bring ln(4) to the other side
over here.
So this will become
we can factorise x, so this will be
so this as division so
You can leave your answer like this or if
you calculate this. This is equal to
You can try more of this
in the exercise provided.
If you are still confused or has any
question you could always ask your
lecturers in your tutorial session.
So that's it for now. In the next video.
You will discuss a new chapter. Make sure to understand this chapter
properly before that. Until then.
Thank you for your attention.
Have a great day and take care.
