99% of Students Make the Same Mistake on This Problem!

追加: 2026-06-02

[00:00:00]storm the internet. Can you solve this?

[00:00:03]Let me check my time.

[00:00:05]Under 10 second watch.

[00:00:07]We have 5 to the power of K plus 5 to the power of K plus 5 to the power of K is equal to 555.

[00:00:16]We are asked to find the value of K.

[00:00:19]Now, let me show you how to solve this.

[00:00:22]How many K can you see on the board? It is three times um 5 to the power of K.

[00:00:31]Which means each of these is a common factor. So, use one of that to factorize each of these um thing. So, we shall have 5 to the power of K.

[00:00:41]All right. If this divide this, we shall have one plus this divide this, we shall have one plus this divide this, we shall have one. All of this is equal to 500 and what? And 55, right?

[00:00:55]Now, 1 + 1 + 1 is 3, which um means we shall have 5 to the power of K multiplied by 3. All of this is equal to 500 and what? And 55.

[00:01:09]Now, I don't want this three to be in the left hand side. So, what do I do? I divide both side by three. So, I shall have 5 to the power of K multiplied by 3 to be equal to 555.

[00:01:24]Divide both side by three.

[00:01:28]So, this will cancel out. We shall have 5 to the power of K to be equal to Now, 555 divided by 3 is 185.

[00:01:40]Interesting.

[00:01:42]But, we cannot express 185 to be in the base of five.

[00:01:48]What do I do?

[00:01:50]Let me show you how to solve this.

[00:01:53]Now, we are going to introduce um logarithm to both side in place of five.

[00:01:59]All right, let us introduce logarithm to both side first. So, we shall have taking the log of both side, log five to the power of K is equal to the log of 185.

[00:02:14]Now, according to the law of logarithm, this K can multiply everything here, which means we shall have K log of five is equal to the log of 185.

[00:02:29]Divide both side by log five to find the value of K.

[00:02:33]Now, if we divide here by log five and also divide here by what? Log five.

[00:02:42]This will cancel out. Now, K will be equal to the log of So, K K will be equal to the log of 185 divided by the log of five.

[00:03:06]Now, watch this.

[00:03:10]If I have something like this, or you can leave your answer like this. But, you can further simplify this. But, as for me, let me leave my answer in this form. You can further simplify because um five times 137 can separate this. But, as for me, let me keep my K to be the log of 185 divided by log of five. Thank you for watching. Share, follow, and subscribe for more math tips like this.