i solved this by using graph f(x) = 2-x and g(x) = 2^(-x) = (1/2)^x f is decreasing linear function g is decreasing exponential function when you graph this two functions they will have two points of intersection. x=-2 or x≈1.7
I kept this at powers of 2 and finished with (x-2).2^(x-2) = -2^(-2) = -4.2^(-4) So (x-2)=-4 x = -2 I can see there is a solution between 1 and 2 also.
Start with 2-x =2^(-x) Let y=2-x then y=2^(y-2) or y=(2^y)/4 or 4y=2^y. Let z=4y then z=2^(z/4) or z=(2^.25)^z. Taking ln of both sides and dividing by z gives ln(z)/z =ln(2^.25). Let c=ln(2^.25)=.173286 Using Lambert app z= -W(-c)/c so that z=16 and z=1.239627 (approx) y=z/4 and x=2-y so x=-2 and x=1.69009 (approx).
erm?... thers only one real solution of X and its not -2 .. X is aproximately equal to 0.543 The straight line y=-x +2 and the cuve f(y)=2^x will intersect eachother at exactly one point [0.543, 1.457] 1.457 = -0.543 + 2 -and 1.457 = 2^0.543 i dunno what the guy in the video tries (misusing lambda function i presume) ..the kind of guy that proves 1+1=3 ...
i solved this by using graph
f(x) = 2-x and g(x) = 2^(-x) = (1/2)^x
f is decreasing linear function
g is decreasing exponential function
when you graph this two functions they will have two points of intersection. x=-2 or x≈1.7
🔥🔥🔥
I solved it before I watched! I got the wrong answer and I tried again and I got the right answer!
You're really amazing!
Wow, thank you! ❤️
🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥
Thanks!
👍
x=-2
I kept this at powers of 2 and finished with
(x-2).2^(x-2) = -2^(-2) = -4.2^(-4)
So (x-2)=-4
x = -2
I can see there is a solution between 1 and 2 also.
Start by raising both sides as powers of 2
2^(2- x)=2^(2^(-x))=(2^(-x))^2
Gives a simple quadratic in 2^(-x)
Leading to x = -2
How did you get 2^(2^(-x))=(2^(-x))^2 ?
@@SyberMath maybe I mistyped but I believed (x^a)^b = x^(ab) = (x^b)^a. Covered it … happy to know if i went wrong
Start with 2-x =2^(-x) Let y=2-x then y=2^(y-2) or y=(2^y)/4 or 4y=2^y. Let z=4y then z=2^(z/4) or z=(2^.25)^z. Taking ln of both sides and dividing by z gives
ln(z)/z =ln(2^.25). Let c=ln(2^.25)=.173286 Using Lambert app z= -W(-c)/c so that z=16 and z=1.239627 (approx) y=z/4 and x=2-y so x=-2 and x=1.69009 (approx).
Wow!
Yes i can
Solve (sinx)^(cosx) = 2
www.wolframalpha.com/input?i2d=true&i=Power%5B%5C%2840%29sinx%5C%2841%29%2Ccosx%5D%3D2 😁
(√3-√2)^x+(√3+√2)^x=(√5)^x
erm?... thers only one real solution of X and its not -2 ..
X is aproximately equal to 0.543
The straight line y=-x +2 and the cuve f(y)=2^x will intersect eachother at exactly one point
[0.543, 1.457]
1.457 = -0.543 + 2 -and 1.457 = 2^0.543
i dunno what the guy in the video tries (misusing lambda function i presume)
..the kind of guy that proves 1+1=3 ...
It's 2^-x, not 2^x. Just plug -2 into the equation and you notice that it is in fact correct
((W(-ln2/4))/ln2)+2
x=2+(W(-ln2/4))/ln2=1,69...
x = -2