A Tricky Algebra Challenge You Should Try!

本站添加: 2026-06-01

[00:00:00]Most students can also this. In this video, I'm going to reveal the secret on this equation.

[00:00:07]Pay close attention to this. You will love the solution to this equation. Now, let's write down the solution.

[00:00:14]Now, the equation says x to the power of x to be equal to 2 to the power of 8 + 2 x.

[00:00:22]Now, from the law of indices, we shall expand this. If you have a to the power of x + y, we can rewrite this as a to the power of x multiplied by a to the power of y. That is what the law of indices state. Now, we shall apply this law in this place, which give us our x to the power of x to be equal to 2 to the power of 8 multiplied by 2 to the power of what? 2 x.

[00:00:49]Now, watch this.

[00:00:51]I can rewrite this as x to the power of x to be equal to 2 to the power of 8 multiplied by um 2 to the power of x.

[00:01:01]Sorry, 2 to the power of 2 all to the power of x. So, that 2 to the power of 2 will give us 4, which become x to the power of x to be equal to 2 to the power of 8 multiplied by 4 to the power of x.

[00:01:17]Now, what we are going to do next is let us divide both side by 2 to the power of 8. So, if we do so, we shall have x to the power of x to be equal to 2 to the power of 8 multiplied by 4 to the power of x divided by 2 to the power of of 8.

[00:01:34]Okay, sorry.

[00:01:36]Divide here by 4 to the power of x and divide here by 4 to the power of x.

[00:01:42]So, if we do so, observe this will cancel out. So, we shall have x to the power of x divided by 4 to the power of x is equal to 2 to the power of 8. So, let us apply the law of indices. From here, if you have a to the power of b divided by uh let me say c to the power of b. We can rewrite this as what? a over c all to the power of b. So, we shall apply this law in this place and let's see what we shall have. That means this become um x over 4 all to the power of x from this law of indices to be equal to 2 to the power of 8.

[00:02:25]Now, watch this.

[00:02:27]If you have um I want to express this two in this fraction in the fractional form.

[00:02:35]What do I do? Of course, we know that 8 um divided by 4 will give us what? Will give us 2. So, I shall replace this two with 8 over 4, which means uh x over 4 all to the power of x will be equals to So, instead of this two, I shall replace that with 8 over 4 all to the power of what? 2. Now, look at this.

[00:03:00]This is x and this is 8, right?

[00:03:04]This is 4 and this is 4.

[00:03:07]This is x and this is 2.

[00:03:10]Sorry.

[00:03:12]And this is 8.

[00:03:16]This is x and this is 8 and this is x and this is 8. So, by comparison, we can confirm that our value of x equals what?

[00:03:24]8. So, this happens to be our amazing solution. Share this video, follow us, and subscribe for more math tips like this. Thank you.