One Simple Trick to Solve This Viral Exponential Equation

Added: 2026-05-10

[00:00:00]can not solve this equation on the board.

[00:00:03]This equation is very very interesting and I believe you will love the solution to this equation. So, by the end of this video, you will know the solution the answer to this equation. So, follow me step by step as I proceed to solve this together.

[00:00:15]Now, we have 1 over x + 2 is equal to 2 to the power of -x. So, we are asked to find the unknown value of x. Whenever you come across this, this is the simplest way and the shortcut method to solve this.

[00:00:26]Now, from the law of indices, we know that if you have a um 1 over a, this can be written as what? As a to the power of -1.

[00:00:38]All right? So, what we are going to do is that we are going to transform this, okay, which is written in this form to this form.

[00:00:45]Okay? So, this equation become x + 2 all to the power of -1. Okay? This is equal to Now, do you believe that this can be written as 2 to the power of x all to the power of -1? Because if you multiply this by this, you are getting -x.

[00:01:08]Right?

[00:01:09]Now, we are going to also um bring out the law of indices that will help us to simplify this. Okay? Because if you have a to the power of x to be equal to b to the power of x. Okay? So, we can say that a is equal to b because the powers are the same.

[00:01:29]Now, look at this. We have -1, we have -1 here. So, we can equally say that x x + 2 is equal to what? 2 to the power of x.

[00:01:40]Now, we still have something to do in this equation because we have a power of x.

[00:01:45]And we need to clear power of x in this equation.

[00:01:48]How can we clear the power of x? You can clear the power of x by multiplying both side by 1 over x. That is the reciprocal of 1 over x. So, we shall have multiply both sides by 1/x, we shall have x + 2 all to the power of 1/x to be equal to 2 to the power of x all to the power of 1/x. So, we want to clear the power of x. So, this can cancel out this. You are left with x + 2 all to the power of 1/x will be equal to 2.

[00:02:24]Now, note if you have the square root of the square root of 4 this can be written as what? 4 to the power of minus 2. I will also notice that the square root of 4 is what? 2.

[00:02:39]So, permit me to write this 2 as 4 to the power of 1/2.

[00:02:42]Okay, so we shall have x + 2 all to the power of 1/x is equal to uh 4 to the power of 1 over 2.

[00:02:56]Now, do you believe that we can split this 4?

[00:03:00]We can uh split this 4 to 2 + 2. So, this equation become um x + 2 all to the power of 1/x is equal to 2 + 2 all to the power of 1 over 2.

[00:03:17]Now, I want to compare something in this equation. We are not equating the base or the powers.

[00:03:22]We are doing comparison to check whether the value of x is correct in this equation.

[00:03:27]So, this is 1/x and this is 1/2. This is x + 2 and this is 2 + 2. So, from the power, let's check what will be the value of x.

[00:03:36]So, we say that 1/x will be equal to 1/2.

[00:03:41]If you cross multiply, x * 1 is x.

[00:03:46]1 * 2 is 2. So, the value of x here is 2. That is for the power.

[00:03:51]Now, for the base, we have x + 2 to be equal to 2 + 2. Of course, we know that 2 + 2 is 4.

[00:03:59]So, we shall have x + 2 will be equal to 4.

[00:04:03]Then, x + x Let's collect like terms. That is, x is equal to 4 - 2.

[00:04:11]So, x will be equal to 4 - 2 is 2. So, the value of x is equal to 2 because both the power and the base satisfy this equation. So, if this is the first time you come across my video, kindly subscribe, share this video, and follow us for more math tips like this.