As you showed by each function (1/2)^x or 2^(-x) is a decreasing function meeting with the linear line functiom (1)(x + 6) that increases in the same intervals. The play with W Lambert function on the ratio to the power eaualling the linear line was interesting! ☺️👍
@RudySchmidt-i7c8 ай бұрын
I taught high school math for 35 years so I recognize an excellent teacher. Over the past year or so I am so impressed with your ability to explain complex ideas in an easily understood fashion. Yes I should join your site because I try a lot of your questions and then watch your approaches to the solutions. I particularly like your multiple solution approaches with a graphical approach at the end. I am a math major and must admit I never heard of Lambert's function before seeing you applying it. Very cool.
@eureoma5788 ай бұрын
this was very beautiful
@SyberMath8 ай бұрын
Thank you!
@giuseppemalaguti4358 ай бұрын
x=(W(64ln2)/ln2)-6=4-6=-2
@ZipplyZane8 ай бұрын
I was glad to see you work out what W(n) was without Wolfram Alpha. With x being an integer, I knew there had to be a way. One thing about how my brain works: I would have just divided ln16/ln2 = log_2(16) = 4. Probably because I never knew about being able to move log down until I started warching your videos. I passed freaking Calculus without ever using ln(2^x) = xln2.
@SyberMath8 ай бұрын
Glad to hear that! Thanks for your comment
@walterwen29758 ай бұрын
A Non-Standard Equation: (1/2)ˣ = x + 6; x = ? (1/2)ˣ = 1/2ˣ = x + 6, 2ˣ(x + 6) = 1; x < 0 Solving the exponential equation using Trial-and-error math: x = - 1: 2ˣ(x + 6) = (- 1 + 6)/2 = 5/2 > 1 x = - 3: (- 3 + 6)/8 = 3/8 < 1; - 1 > x > - 3 x = - 2: 2ˣ(x + 6) = (- 2 + 6)/4 = 1; Proved Answer check: (1/2)ˣ = x + 6; Confirmed as shown Final answer: x = - 2
@farhansadik54238 ай бұрын
Awesome!
@SyberMath8 ай бұрын
Thank you! Cheers!
@michaelbaum67968 ай бұрын
Very nice equation- thanks a lot👌
@SyberMath8 ай бұрын
Glad you liked it
@mcumer8 ай бұрын
I found x=-2 and it is the only one solution because y=x+6 is an increasing funcion while y= 1/2 is a decreasing funcion
@Mehrdad_Basiry-fj4rl8 ай бұрын
So amazing... learn alot...❤❤❤.
@SyberMath8 ай бұрын
Thank you so much 😀
@robot83248 ай бұрын
On the first look of it I used -2 😆
@scottleung95878 ай бұрын
I also got -2 as the only solution.
@johnpinckney72698 ай бұрын
nice
@SyberMath8 ай бұрын
Thanks
@sunny_258 ай бұрын
X=-2....is the only solution... Verified graphically