Only 1% Can Solve This Exponential Equation! | Find x Challenge

[00:00:00]Let me show you how to solve this amazing haha um math Olympian the board. This is not simple as you think. But in this video, I'm going to explain the step-by-step approach to to get the the value of Y. It's just so simple. Watch this.

[00:00:16]Now we have 5 to the power of - X equal to 6 + X.

[00:00:21]What must be the value of X? Of course, we know that this all of this is in exponential form, while this is what? In linear form.

[00:00:30]So now, just watch.

[00:00:33]Can we say let Can we say let um let us use Y Y to be equal to 6 + X.

[00:00:45]So if Y is equal to 6 + X, what is X?

[00:00:49]So we can swap the side and we shall have um 6 + X equal to Y. Okay. So our Y our X will be equal to Y Y 6 cross over we shall have - 6.

[00:01:05]So just watch this.

[00:01:07]Our Y is equal to 6 + X.

[00:01:10]But our X is Y - 6.

[00:01:13]So what is our X here? Our X is Y - 6.

[00:01:16]So we shall have this equation becomes let us substitute this um into the given equation and see what we shall have, right? So we shall have 5 to the power uh to the power of minus what is our X? Our X here is Y - 6. So we shall have into Y um X is Y - 6, right?

[00:01:38]To be equal to 6 + X is what?

[00:01:42]6 + X is equal to what? Y.

[00:01:47]So let us open up the bracket.

[00:01:50]This bracket here, right? So by multiplying minus times Y, so we shall have 5 to the power of minus times y is minus y, right?

[00:02:02]Minus minus is plus, so we shall have plus six. All of this is equal to what?

[00:02:07]One.

[00:02:09]What next?

[00:02:11]Of course, this y has a natural power of one. We all know that this y has a natural power of one.

[00:02:17]So, I am looking for a way to clear this minus y in the left-hand side because y cannot be on both sides.

[00:02:26]Okay? So, now to get to clear this minus y, let us add y to both sides of the equation, okay? So, if we add y to both sides of the equation, we shall have 5 to the power of minus y plus six plus y, okay?

[00:02:45]To be equal to y to the power of one plus y. What we just did here is that we are adding y to both sides. So, observe something that um this minus y will cancel out this plus y. So, we we are going to be left with 5 to the power of six to be equal to y to the power of one plus y.

[00:03:10]Okay?

[00:03:11]Now, what next?

[00:03:13]We are looking for a way also to clear this one.

[00:03:19]So, let us let us try to um subtract one from both sides.

[00:03:28]Let us subtract one from both sides and see what we shall have. So, if we do that, this equation becomes Let me take it over here. So, we shall have 5 subtract subtract one from like both powers, right?

[00:03:46]From from both both powers, right?

[00:03:54]So, let's see what we shall have if you subtract one from both powers like these powers above it. So, we shall have 5 to the power of 6 minus one, right? To be equal to y to the power of one plus y minus one. So, what what we just did is that we are subtracting um one from both powers, right?

[00:04:18]Now, this 1 minus 1. So, this one will cancel out this minus 1, right?

[00:04:24]6 minus 1 is 5, so we shall have 5 to the power of 5 to be equal to y. What is left is y to the power of one, y.

[00:04:36]So, for example, if you have a let me say if you have a to the power of a to be equal to b to the power of b, this implies that our a what is equal to b.

[00:04:48]So, from here we we can just confirm that y itself is equal to 5.

[00:04:54]But, we are not asked to find the value of y. We are asked to find the value of x.

[00:04:59]But, from this given statement we we declare that x our x our x is equal to y minus 6.

[00:05:09]Our x is equal to y minus 6. So, what Since our y is 5, this equation becomes x equals 5 minus 6.

[00:05:20]So, we can just say that 5 minus 6 is um minus one, right? So, our x will be equal to minus one. So, the value of x is minus one. This is how to solve this amazing math equation. Thank you for watching. If this video is interesting and you enjoyed this class, do as well to share this video and subscribe to this channel for more math tips like this. Please like