Can you solve xˣ = 100? This is a tricky math challenge!

This looks impossible, but let's do it together and see. because 1 squared is actually equal to 1 times 1, right which is 1 and 2 squared is 2 times 2 Which is 2, which is 4, rather. Then we have 3 to the power of 3. is equal to 3 times 3 times 3 which is 27. It's still not up to 100 right now. if we say 4 to the power of 4 and this will be 4 times 4 times 4 times 4. So this is the same as 16 multiplied by 16, and that's 16 squared right now. Let's use a A a yat ki ni ye pure Sixth month of the year is June. 1 Shuyu Chu Ro Ro 1 times 6 is 6, 6 times 2 is 12, so it's going to be 256. I have these math strips in this channel, Just check one of my playlists, Math Strips. And you're going to see a lot of them. Like this, so the answer is 256. so we have 256. Now we are looking for a number raised to the power of itself that the answer will give us 100. And we can see that the answer lies between 3 and 4, right? So, it means that 3 is less than x. which is less than 4. So, it means that our answer is a decimal between 3 and 4. Now how do we find its value? if this is the first time you have seen this wonderful channel Please click the subscription button and turn on your notification bell. so that you don't miss my videos I upload my videos as often as possible, tune In at your confidence there must be something new for Give us a thumbs up if you love what we're doing and most importantly, please drop your Comments: Yeah, I really need that. Let me know how I'm doing. In the comments section, okay Because we have x to the power of x, Let us add a line to both sides of this equation. So, if we draw a line to both sides, we will x raised to the power of x is equal to 100. Now, note that line a to the power A is equal to line A. This comes down. to multiply ln a, therefore we can Now write this equation, this one. As x ln x equals ln 100 Now, 100 is equal to 10 squared. Okay, so we can now write this as ln. x is equal to ln 10 to the power Now, applying this rule as well, We're going to write this as 2 ln 10, right? So, we have x ln x is equal to 2 ln 10. Nice. Now, there is something you need to know. What is equal to e raised to the power of ln x, right? Yes, x is equal to e raised to the power of ln x. And that means that I can write this for me to erase it, which means that that I can write this equation as x is e ln x, so now we have e ln x multiplied ln x multiplied by ln x equals 2 In 10, okay, 2 ln 10. Don't worry, we're almost We're almost done with this. So, I want to say a big thank you to all my supporters, especially my old subscribers who have been there all along to support me. Thank you very much. Okay, now this is what we have. Now, we can write this as ln x. e raised to the power of ln x equals 2 times ln 10. Now, remember. The lambda w function, I love that function so very much the lambda w function it says that when you take the lambda w function e to the power of a right that this is equal to a Now take a look at what we have here—you can see that we can do something like this, there so if we take the lambda w function On both sides we have ln x e ln x is equal to 2, okay, lambda w function of 2, and then 10, okay so from here, if you compare this and this You can see that our a is equal to ln x, right? simply means that this side will give us what ln x, since this is equal to a, then this will give us ln x so we are going to have ln x is equal to to the double number function. Off to Okay, now also recall that x is equal to e to the power of ln x, right? So if we take, if we put raise e to both sides of this equation right so we are going to have e to the power of ln x is equal to e to the power of lambda times w function of 2 lambda times 10. Hmm, amazing. Now this will give us x, right? Is equal e to the power of the lambda w function In 10 now x is equal to with your calculator Okay, this will give you 3.57 And that's the answer, thank you. So much for watching, and see you in my next video. Bye.