A Non-Standard Equation | Math Contests

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[@lawrencejelsma8118]

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! ☺️👍

[@user-qr5gy2kp7e]

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.

[@eureoma578]

this was very beautiful

[@SyberMath]

Thank you!

[@robot8324]

On the first look of it I used -2 😆

[@giuseppemalaguti435]

x=(W(64ln2)/ln2)-6=4-6=-2

[@mcumer]

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

[@scottleung9587]

I also got -2 as the only solution.

[@farhansadik5423]

Awesome!

[@SyberMath]

Thank you! Cheers!

[@michaelbaum6796]

Very nice equation- thanks a lot👌

[@SyberMath]

Glad you liked it

[@Mehrdad_Basiry-fj4rl]

So amazing... learn alot...❤❤❤.

[@SyberMath]

Thank you so much 😀

[@ZipplyZane]

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.

[@SyberMath]

Glad to hear that! Thanks for your comment

[@johnpinckney7269]

nice

[@SyberMath]

Thanks

[@rakenzarnsworld2]

x = -2

[@sunny_25]

X=-2....is the only solution...
Verified graphically

[@reckless_r]

Geographycally

[@walterwen2975]

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

[@reckless_r]

Lnlnlnlnlnlnlnlnonlnlnknonlnlnlnlnlnlnlmpbknlnlnlnlnlnlnlnlnlnlnlnlmlnlnlnlnlnlnlnnllnlnlnlnlklnljlnlnlmnklnnlmnnllnnnlmnnklnnnnnnnnnnnnnnnnnnnnnnnlllllllllllbbnnnnnnmnm

[@SyberMath]

😮😜😁

[@marwansal4175]

Most important lesson here: manipulate equations but NOT people 🤗😔