Japanese| A Nice Math Olympiad exponential problem| solve for x

Shall we solve this together? Now, we have that 2 raised to the power of x is equal to x raised to the power of 4. and we are asked to find the value of x. Alright, this is the trick. All you need to do is multiply x by 4. That's 4 times x, right? Raise each of them to the power of 1 over x multiplied by 4. So we are going to raise this side to the power of 1 over x multiplied by 4. On this side, we are also going to do the same thing. x raised to the power of 4 raised to the power of 1 over x multiplied by 4. Then, recall the exponent law that states that a to the power of m raised to the power of what? n is equal to a to the power of m multiplied by n. So we are going to do that here. If we do that here, that means this is the same thing as 2 to the power of x. I might mind my own space. 2 to the power of x multiplied by 1 over x to the x multiplied by 4, right? Is equal to x to the fourth power multiplied by 1 over x multiplied by 4. Now your x, we divide x. Then in this case, you have 2 to the power of 1 multiplied by 1 over 4. Now, in this case, you have x to the power of Because this 4, we divide this 4. You have x to the power of 1 over x. Alright. Now look at this here. This one, alright? We can rewrite this 1 as 4 over 4, right? Multiplied by one over four. And this is equal to x raised to the power of 1 over x. Alright. Now we can express this as what? 2 raised to the power of 4 times 1 is 4. Or just 4 multiplied by 1 over 4 times 4 is what? 16. Is equal to x raised to the power of 1 over x. Alright. 2 raised to the power of 4 is 16. 16. So we have 16 raised to the power of 1 over 16. Is equal to x raised to the power of 1 over x. Now, by comparison, we have 16x. We have 16 and x again. Therefore, our x is equal to what? 16. Don't forget to subscribe and turn on your notification bell. so that you'll be notified whenever I upload a new video. Goodbye.