Algebra Lesson: Solving Hard Exponential Equations

Added: 2026-05-11

[00:00:00]The method I'm going to use to solve this equation will amaze you.

[00:00:04]Nobody has ever shown this to you. I believe you are going to learn a new thing today.

[00:00:09]We have 3 to the power of x is equal to x to the power of 9.

[00:00:13]This method is very very simple for you guys.

[00:00:17]Now, what we are going to do is that let's say let um x to be equal to 3 to the power of y.

[00:00:26]Okay? So, let x equal to 3 to the power of y. Then let's put in 3 to the power of y in this equation and see what we shall have. Anywhere you see our x, put in 3 to the power of y.

[00:00:37]Okay? So, this become 3 to the power of over our x here is what? 3 to the power of y. So, this is 3 to the power of y is equal to this x is what?

[00:00:48]3 to the power of y all to the power of 9.

[00:00:54]Okay? So, this become Look at this.

[00:00:58]9 * y is 9y. So, this become 3 to the power of 3 to the power of y is equal to 3 to the power of 9 * y is 9 y.

[00:01:14]All right? Now, let's consider this law of indices.

[00:01:17]If you have a to the power of b to be equal to a to the power of c, this implies that b is equal to c.

[00:01:29]Now, from here, this equation become 3 to the power of y is equal to 9 y.

[00:01:38]Let me show you how to solve this.

[00:01:40]What we are going to do is that let's divide both sides by 9. So, if I divide No, by y. So, if I divide here by y and also do the same to the left hand side, this will cancel out this. This become um 3 to the power of y divided by y is equal to 9.

[00:02:00]Now, what next?

[00:02:03]I want to express the left hand side to be like the right hand side. How can I achieve that? And we all know that this 9 can be expressed as 27 divided by 3.

[00:02:15]So, we shall have um 3 to the power of y divided by y to be equal to instead of this 9, put in your 27.

[00:02:26]Okay, divided by 3.

[00:02:28]Because 27 divided by 3 will give you what?

[00:02:32]Um sorry, 21.

[00:02:37]3 Sorry, 27. Sorry, 27 to the power 23 27 divided by 3 is 9. Okay? Because 9 * 3 is 27.

[00:02:45]Now, look at this. This 27 can also be written as 3 to the power of 3. So, this become our 3 to the power of y over 9 Sorry, over y is equal to 3 to the power of 3 by 3.

[00:02:58]Now, from the from the numerator, if I say 3 to the power of y to be equal to 3 to the power of of 3, this implies that our y is equal to 3 from the numerator. From the denominator, we can say that our y is just equal to 3.

[00:03:13]So, we we have obtained our solution of y to be equal to 3. So, from the given equation, we say x Our x is equal to 3 to the power of y, but our y is 3. So, let's put it back and see what we shall have.

[00:03:26]So, our x will be equal to 3 to the power of 3, which implies that our x also therefore our x is equal to 27. So, this happens to be our final answer. I believe this method is very simple for you and you can access this question in a very simple way. Help us to share this video, follow us, and subscribe to our channel. Thank you.