Looking at the thumbnail, I expected the problem to be a real chore, and beyond my limited capabilities. However... I intuitively went for the second method (the exact steps I took were slightly different from yours, but it was essentially the same) and, to my surprise, I reached the solution within about 45 seconds. These videos are causing me to improve quite a bit. Thanks a bunch.
9^((1-x)/2x) = 3^((1-x)/x) = 3^(1/x - 1) So 5 = 3^(1/x - 1) Multiply both sides by 3 to get: 15 = 3^1/x Now raise both sides to the power of x and get 15^x = 3
Instead of taking xth root of 3,just raise both sides to power x and then express 3^1-x =5^x as 3 /3^x=5^x. Then you cross multiply and get your answer.
The first equation gives after making 9=3² and taking the ln: ((1-x)/x)ln3=ln5. Plug this in for ln5 in ln?=xln3+xln5. This gives ln?=xln3+(1-x)ln3=ln3. So ?=3.
I used the second method - couldn't believe how easy and quick it was!
Looking at the thumbnail, I expected the problem to be a real chore, and beyond my limited capabilities. However... I intuitively went for the second method (the exact steps I took were slightly different from yours, but it was essentially the same) and, to my surprise, I reached the solution within about 45 seconds. These videos are causing me to improve quite a bit. Thanks a bunch.
Glad to hear that!
The first method is like walking through a garden of log rules. 😁
I loved the way you dealt with the exponents!
I would have solved this exercise using the 2nd method
9^((1-x)/2x) = 3^((1-x)/x) = 3^(1/x - 1)
So 5 = 3^(1/x - 1)
Multiply both sides by 3 to get:
15 = 3^1/x
Now raise both sides to the power of x and get
15^x = 3
Yesssss !!!!! I used the second one !
The first method allows you to determine the value of x. The second method shows that you do not need to do that to find 15^x.
Instead of taking xth root of 3,just raise both sides to power x and then express 3^1-x =5^x as 3 /3^x=5^x. Then you cross multiply and get your answer.
I did it on my first try really
Nice
The first equation gives after making 9=3² and taking the ln: ((1-x)/x)ln3=ln5. Plug this in for ln5 in ln?=xln3+xln5. This gives ln?=xln3+(1-x)ln3=ln3. So ?=3.
Thank you.
The solution will be shorter if we take the logarithm not by base e, but by base 15. We will immediately get x = log 3
15
Omg, obviously the second method.
I calculated in my head up to 15^(ln3/ln15), the calculator gave 3. It was good...
3, very easy😊
Great 👍
Answer: 3
Very very well and thank you for your video master
interesting
Easy
3
3.
3