This was a neat little problem. I didn't imagine the process for solving it would be so complex at first glance. This was my first time seeing the Lambert W function. Thanks for taking the time to share it.
Also, we can say that both sides are 2 functions. The first function is exponential. The second is direct proportion function. The first function decreases, since the base is less than 1, and the second function increases because it is positive. Both of these functions intersect at one point and by selection we can find that it is 2
This was a neat little problem. I didn't imagine the process for solving it would be so complex at first glance. This was my first time seeing the Lambert W function. Thanks for taking the time to share it.
You are most welcome! ❤
Also, we can say that both sides are 2 functions. The first function is exponential. The second is direct proportion function. The first function decreases, since the base is less than 1, and the second function increases because it is positive. Both of these functions intersect at one point and by selection we can find that it is 2
Very nice! ❤
👍👍👍
Thanks for liking! ❤
Math Olympiad: (1/2)ˣ = x/8; x =?
(1/2)ˣ = 1/(2ˣ) = x/8, x(2ˣ) = 8 = 2(4) = 2(2²); x = 2
Answer check:
x = 2: (1/2)ˣ = (1/2)² = 1/4, x/8 = 2/8 = 1/4; Confirmed
Final answer:
x = 2
Very nice! ❤
2, by inspection.
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Took 10 minutes for just 30 seconds problem 😅
Sorry for inconvenience! ❤
2
Very nice! ❤
Quanta sofisticação. Problema morre onde x.2^x = 2.2^2 logo x = 2.
Enrabação de mosquito.
wdym i just used the good ol’ guess and check method and found it’s just 2
Very nice! ❤
Kua hall hai
I am fine, How are you?
8(2^-×)=×
=>8=×.2^×
=>W{× ln2.e^ln2(×)}
=W{2ln2.e^ln2(2)}
=>×ln2=2ln2
=>×=2
Very nice! ❤