The Math Olympiad Question Anyone Can Solve (With This Trick!)

Added: 2026-05-10

[00:00:00]touched the solution to this equation. I am going to show you every bit of a step I am taking to get my final answer. So the question reads as 5 to the^ of x or 5 / the roo<unk> of 5 all to the^ x is equal to 25.

[00:00:18]Now to solve to solve this observe that this x or this bracket covers up this fraction which means that this x belongs to five and root of five.

[00:00:30]But before we proceed there is something that we need to reduce which is the root of five because among this equation the complex form of a team is the root of five. So root of five need to reduce first before any other thing. So to reduce this we are going to introduce a lot of indices that will help us to to reduce this um sort.

[00:00:56]Now look at this. If you have the square root of a this can be written as a to the^ of 1 / 2.

[00:01:07]So this will help us to reduce this which means we shall have 5 / 5 to the^ of 1 / 2. This five has a natural power of 1 all to the power of x is equal to 25.

[00:01:28]Now look at this. This is five and this is five.

[00:01:33]Yes. Then if this is true, this five is dividing this five. Then let's recall a law of indices that will help us to solve this. And that law of indices state that if you have a to the power of b divide um dividing b or a to the power of c. This is the same thing as saying a to the power of b minus c because the same base is dividing.

[00:02:02]So what am I trying to do? I'm trying to reduce this fraction which means we can express this as 5 to the^ of 1 - 1 / 2 to be equal to 25.

[00:02:18]Most students cannot reduce this cannot solve this. Let me show you how to solve this fraction first.

[00:02:27]Now we have 1 - 1 / 2.

[00:02:31]You can call this over one for the sake of your LCM.

[00:02:35]The LCM here is 2. 2 / 1 is 2 * 1 is 2.

[00:02:41]You put a minus. 2 / 2 is 1 is 1. 1 * 1 is 1. So 2 - 1 is 1 / 2. So whenever you are you are subtracting a half from one you always have and half which is 1 / two. So of course this become 5 to the power of 1 / 2. Remember I supposed to cover this with all to the power of x which means this is all to the power of x to be equal to 25.

[00:03:25]This fraction can multiply this x. We shall have 5 to the^ of x / 2 is equal to 25.

[00:03:36]Now look at this. This 25 can be expressed in the base of five.

[00:03:41]Then we shall have 5 to the^ x / 2 is = 5 ^ 2.

[00:03:49]The same base we shall have x / 2 is = 2. For the sake of cross multiplication call this over one then you cross multiply.

[00:04:02]This cross multiply x * 1 is x which is equal to 2 * 2 is 4. So our final answer is four.