A Nice Math Olympiad Exponential Problem | Japanese | how to solve for "x".

Very well, you'll be able to tackle it. Okay, so let's start by discussing those laws of indices. that we are going to apply here, welcome back to my channel. If this is the first time you're tuning in, just stay tuned because you're going to enjoy the ride, and if you are a returning viewer, just Know that you're most welcome; just take the front seat, okay? All right, um, let's start. The first thing we need to discuss is let's start with the numerator, okay? Um, the law of indices. states that when you have a to the power of x okay times a to the power of y times a to the Power of z: okay, once they have the same base, just pick one base and then add the exponents x plus y plus z okay, let's apply this law to the numerator, okay? um, so we can rewrite the numerator as Nine, we're going to pick one base. Um, I'm trying to figure out how to use this board well, so let's apply that to this; for the numerator we are going to write, we are going to pick one base, which is nine, and we are going to add all the powers: nine plus nine plus nine, okay, divided by now for the denominator the denominator we have nine to the power of nine plus nine to the power of nine plus nine to the power of nine is just like saying a plus a plus a, okay, and when you have something Like this is what three A is, just like saying, um, mango plus another mango plus another. Mango, okay, we should give you three mangoes, right? So that means this is the same thing as three what nine to the power of nine okay is equal to nine to the power of x so this is nine nine to the power of three gives us 27; that is, nine plus nine is 18, and 18 plus nine Is 27 over three to the power of what nine three times nine to the power of nine, which is the same thing as nine which is equal to nine to the power of x I'm on nine nine nine nine okay now let's Continue; we can decide to change them and put them on the same base, okay, because this is exponential. question and the best thing you can do for yourself when you have such a question is to try to put them in the same base, so we can write this nine as three to the power of two, so write that this two to the power of 27, okay, divided by three, brackets, three to the power of what, two nine raised to the power of what is equal to three to the power of two raised to the power of x; if we solve this further, anytime you have something like this You have two exponents on a number; you must multiply the exponents according to the law. of indices, so we can write this as three raised to the power of two times 27 and two times 27 will give us 54, and in this case, this is the same thing as three times what—three raised to The power of two times nine is 18, okay, is equal to three two times x is 2x, okay, now this is equal to 54 divided by you need to be careful here, yes, you have to, but before that, if this is the If this is your first time encountering this lovely channel, it's time for you to hit that button. Click the subscription button and then click the notification bell so that you'll be notified Whenever I upload a new video, please comment and let me know what you think about what I'm doing. And please provide another solution if you have one, and above all, I truly want to thank you. Those who normally provide different solutions to what I solve know how highly you are appreciated. Okay, now recall what I said at the beginning: when you have the same base, you do what? You pick one base; know that this same thing is three to the power of one, okay? So one plus 18. is equal to 3 raised to the power of what? 2x. Also, let's apply another law of indices here. and that law states that when you have a number in this form, meaning they have the same base, then They are dividing; all you need to do is subtract the powers. When multiplying, you add them. When dividing, you subtract the exponents, so we can write this as three to the power of 54. -19 is equal to 3 raised to the power of 2x, so this is the same as 3 raised to the power of 54 minus 19. We have 14 minus 9, which gives us 5, and 3 minus 1 and 4 minus 1, which give us 3. so this 3 to the power of 35 is equal to 3 to the power of 2x once you have the same base When you have the same base, you create the powers by doing what you create. So we can write that 35 is equal to 2x. Okay, so we have that 35 is equal to 2x. Let's divide both Divide both sides of this equation by 2, and when we do that, we will have that x is equal to 35 over 2. Thank you so much for watching. You can watch another one please, and have a nice day.