99% Get This Equation Wrong! Can You Solve It?

追加: 2026-05-22

[00:00:00]In this video, I'll be showing you how to solve this kind of exponential equation. I know you are learned that whenever the bases are expressed or whenever the exponents are the same, what do you do? You equal the base. In this case, it's not going to work because three can never be equal to two.

[00:00:15]Instead, let me show you how to solve this. All right. So, we are going to use the laws of indices to break this down, then we get the value of x.

[00:00:24]Now, watch this. I can expand this to become three to the power of x multiplied by three to the power of two.

[00:00:31]Okay?

[00:00:32]To be equal to three to the power of Sorry, two to the power of x multiplied by two to the power of two.

[00:00:42]Because from the laws of indices, whenever you the bases are multiplying the same, what do you do? You add the powers, which result to this and the same thing applicable to the what? The right hand side.

[00:00:52]So, three squared is nine, so we shall have three to the power of x multiplied by nine to be equal to two.

[00:01:00]Um Can you say two to the power of x multiplied by um four?

[00:01:09]Watch this out.

[00:01:10]>> [snorts] >> Now, I I don't want this two to the power of x to be in the right hand side, so let me move it to the what? Left hand side. So, I shall divide both side by two to the power of x and divide this side by two to the power of x, which means this cancel out this.

[00:01:27]Okay? So, we shall have three to the power of x over two of x multiplied by nine to be equal to four.

[00:01:35]Now, watch this.

[00:01:38]Um let me move this nine to this side.

[00:01:41]Like, I want to have a fraction like this. So, what do I do?

[00:01:45]Let me divide both side by nine. So, if I divide here by nine and divide here by nine, you observe that this cancel out.

[00:01:51]You are left with three to the power of x over two to the power of x is equal to this. So, I suppose not to write this as what? As 9. I suppose to write it as 3 ^ 2. So, I'm going to transform from here to this form, right?

[00:02:05]So, we shall have 2 squared divided by what? 3 squared.

[00:02:12]So, when you have the same powers, what do you do? You single out the power. So, we shall have 3 over 2 all to the power of x to be equal to the same thing here, 2 over 3 all to the power of x. Sorry, all to the power of 2.

[00:02:28]Okay?

[00:02:30]Now, watch this out.

[00:02:32]This is 3 over 2 and this is 2 over 3.

[00:02:34]They are not expressed the same what?

[00:02:36]So, what do you do? You apply um you reciprocate this.

[00:02:41]Because there's a law of indices that say that if you have a over b all to the power of c this can be expressed as what? b over a all to the power of minus c.

[00:02:54]So, what do I do here? Let me reciprocate this and it's going to affect the both exponents. So, we shall have 3 over 2 all to the power of x to be equal to 3 over 2 all to the power of minus 2. So, now the bases are now expressed the same. What do you do? You equate the powers. So, x is equal to minus 2 and that's the final answer.

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