99% FAIL This Olympiad Equation 😱 | Can You Solve It?”

Added: 2026-05-23

[00:00:00]you out to solve this math Olympiad.

[00:00:03]So, I want you guys to follow me step by step as I provide a solution to this equation.

[00:00:10]We have 2 to the power of X is equal to X to the power of 4.

[00:00:14]Now, look at this.

[00:00:16]We have a power of X and also have a base of X.

[00:00:20]Now, to solve this, first of all, let us let's raise both powers by 1 over X.

[00:00:29]By doing that, we shall clear the above X in one side. So, we shall have 2 to the power of X all to the power of 1 over X will be equal to X to the power of 4 all to the power of 1 over X.

[00:00:44]So, we shall cancel out this, so we shall have 2 to be equal to X to the power of 4 times 1 over X, we shall have 4 over X.

[00:00:56]We still need to clear the fraction in the right hand side. So, to do that, let us multiply both powers again by um 1 over 4.

[00:01:07]So, we shall have 2 to the power of 1 over 4 is equal to X to the power of 4 over X all to the power of 1 over 4.

[00:01:19]All right?

[00:01:20]So, this four will cancel out this four.

[00:01:23]We shall have 2 to the power of 1 over 4 to be equal to X to the power of 1 over X.

[00:01:32]Now, look at this.

[00:01:33]I can rewrite this two as 2 to the power of 1 all to the power of 1 over 4. This is equal to X to the power of 1 over X.

[00:01:45]I can further simplify this one as 4 divided by 4. So, this become 2 to the power of 4 divided by 4 because 4 over 4 is 1 all to the power of 1 over 4 to be equal to x to the power of 1 over x.

[00:02:02]Now, to continue this in this place, I can bring out 1 over 4 from this 4 over 4.

[00:02:08]So, this become 2 to the power of 2 to the power of 4 all to the power of 1 over 4 multiplied by this 1 over 4, so multiplied by 1 over 4 to be equal to x to the power of 1 over x.

[00:02:30]Okay?

[00:02:32]Now, 2 to the power of 4 is 16. So, this becomes 16 to the power of 1. 4 * 4 is also 16, so this is 1 over 16 to be equal to x to the power of 1 over x.

[00:02:46]Now, let's do comparison in this equation because we want to set the base equal.

[00:02:51]We are not doing that because the bases are are the same, but we just want to do the comparison to confirm the value of x.

[00:02:59]So, if I say 1 over 16 to be equal to 1 over x, of course, when the numerator are the same, what do you do? You just equate x to be equal to what? 16. And that happens to be the final answer.

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