Think you're good at math? Here's an interesting exponential equation that will put your problem-solving skills to the test!
At first glance, this equation might seem straightforward, but finding the value of x requires careful mathematical thinking and a good understanding of exponents.
In this lesson, I'll walk you through the problem step by step, explaining the mathematical approach and showing you how to work towards the solution.
Whether you're a high school student, preparing for the SAT, GCSE,studying algebra, or simply enjoy solving challenging math problems, this lesson is for you.
Before watching the solution, pause the video and see if you can solve it on your own.
What answer did you get? I'd love to read your approach in the comments.
Subscribe to JJ Online Maths Class for more challenging math problems, algebra lessons, math puzzles, and step-by-step tutorials.
Remember, every challenging problem is an opportunity to become better at math.
Hello and welcome back to my channel.
We are asked to find the value of x. Now let's do it together.
First, this is an underexponent
so we actually need to solve it using the exponential rules.
Okay, so x to the power of x equals,
recall that a to the power of n plus n
equals a to the power of m multiplied
by a to the power of n right so we can express this as
3 to the power of x multiplied
by 3 to the power
of 243 now let's divide both sides
divide both sides by 3 to the
power of x so if we do that
We are going to have x to the power of x divided by 3
to the power of x is equal to 3 to the power of x
multiplied by 3 to the power
of 243 divided by 3 to the power of x.
Please subscribe to my channel and turn on the notification bell.
If this is the first time you have seen this amazing channel,
most importantly, drop a comment in the comment section.
If you have a simpler way of solving
this or a faster way of solving it,
don't hesitate to write that.
Tell us what you feel about the video and about the channel.
The good, the bad, the ugly, you will listen.
Okay, thank you.
Now, recall
also this law that says that A over B
a to the power of x over b to the power of x equals
a over b all to the power of x so we can now use
that here so we can rewrite this as x divided
by 3 raised to the power of x is equal to now this
will divide itself we have 1 and 1 times
this is still the same 3 to the power of 243 okay
Now, remember that I said
this is under exponents, right?
We need to use exponential rules to solve them.
So, I want
to raise each side
to the power
of one-third, okay?
Now, if I do that, that means this becomes x over 3 raised
to the power of x raised to the power of 1 over 3.
So, we can rewrite
this as x
over 3 raised
to the power of x
times 1 over 3
is also x over 3,
right?
Is it equal to
Now, here we have 3 to the power
of 243 multiplied by 1 over 3.
So, x over 3 to the power
of x over 3 is equal
to 3 to the power of...
Now, 3 will go into 24 8 times, going to 31.
So, we have 81 here.
If we solve for that...
Are you still there?
Okay.
Okay, so if we solve for the...
We can see that we have the same thing as base and power.
Is there a way we can manipulate this side to get
the same thing as the base and the power, right?
I think there is.
Now, let's go.
We have x over 3 to the power of x over 3
is equal to 3 to the power of...
Now, 81 is same thing as 3 multiplied by 27, alright?
That means that we can rewrite this as
x over 3 to the power of x over 3
is equal to 3 to the power of 3
raised to the power of 27, right?
Let's clean the other side. That place is
small. This time for you
to subscribe if you have forgotten.
Okay, have you subscribed?
Now, I'm going to rewrite this. So this is x
x over 3 to the power of x over 3.
Now, we have x over 3
to the power
of x over 3 is equal
to 3 to the power
of 3 is 27 to
To the power of twenty-seven.
Are you seeing anything?
Now, by comparison, by comparison, you can see that x over 3 equals 27,
right? By comparison,
x over 3 is equal to 27 over 1.
Now, if we cross multiply,
we will have x times 1 is x is equal
to 27 times 3 is 81 and that's the value of our x.
Thank you so much for watching, have you subscribed? Please subscribe,
like, comment and share so that students that are
doing their exams
or have exams to do will see this and learn as well. Thank you
Thank you once more and see you in my next video.
