### Video Transcript

Given that three to the power of π₯
equals 27 and three to the power of π₯ plus π¦ equals 81, find the value of π₯ and
the value of π¦.

Well, thereβre a couple of ways we
go about solving it. One way is to use an exponent
rule. And that rule is a multiplication
rule, which tells us that if we have π₯ to the power of π multiplied by π₯ to the
power of π, itβs equal to π₯ to the power of π plus π. So therefore, using this, what we
can do is rewrite three to the power of π₯ plus π¦ equals 81 as three to the power
of π₯ multiplied by three to the power π¦ is equal to 81.

And now, what we can do is we can
substitute in three to the power of π₯ equals 27 into our equation. And if we do that, what we get is
27 multiplied by three to the power of π¦ equals 81. So, now what we can do is divide
both sides of our equation by 27 to find out what three to the power of π¦ is. When we do that, we get three to
the power of π¦. And thatβs because if we divide the
left-hand side by 27, weβre left with three to the power of π¦. And we get itβs equal to three, and
thatβs because 81 divided by 27 is three.

Well, if three to the power of π¦
is equal to three, therefore π¦ must be equal to one. And thatβs because three to the
power of one is three. Also, we can think about it as if
we equate our exponents at this point, weβd have π¦ is equal to one. So, thatβs our value of π¦
found. And now, we want to find our value
of π₯. Well, we can say that three
multiplied by three multiplied by three is equal to 27. So therefore, three cubed is equal
to 27. So therefore, we can say that π₯ is
equal to three and π¦ is equal to one.

What we can do is quickly check
this. And we can do that by substituting
in π₯ equals three and π¦ equals one into three to the power of π₯ plus π¦ equals
81. So, we do that, weβre gonna get
three to the power of three plus one equals 81, which gives us three to the power of
four is equal to 81. Or, three multiplied by three is
nine multiplied by another three is 27 then multiplied by a fourth three is 81. So yes, this is correct. We can definitely say that π₯
equals three and π¦ equals one.