Can We Solve An Exponential Equation? đ
VloĆŸit
- Äas pĆidĂĄn 2. 08. 2024
- đ€© Hello everyone, I'm very excited to bring you a new channel (SyberMath Shorts).
Enjoy...and thank you for your support!!! đ§Ąđ„°đđ„łđ§Ą
/ @sybermath
/ @aplusbi
â Join this channel to get access to perks:â bit.ly/3cBgfR1
My merch â teespring.com/stores/sybermat...
Follow me â / sybermath
Subscribe â czcams.com/users/SyberMath?sub...
â Suggest â forms.gle/A5bGhTyZqYw937W58
If you need to post a picture of your solution or idea:
intent/tweet?text...
#algebra #exponential #exponentials
via @CZcams @Apple @Desmos @NotabilityApp @googledocs @canva
PLAYLISTS đ” :
ⶠTrigonometry: ⹠Trigonometry
ⶠAlgebra: ⹠Algebra
ⶠComplex Numbers: ⹠Complex Numbers
ⶠCalculus: ⹠Calculus
ⶠGeometry: ⹠Geometry
ⶠSequences And Series: ⹠Sequences And Series
Let f(x) be the left-hand side of this equation. It is easy to show that f(x) is concave up everywhere and has a minimal point at x=0 and f(0)=3.
Nice
easier. by observation the LHS is uniformly increasing with x. Since any positive value to the 0 power equals 1, by observation x must = 0, and no other real solution is possible.
*What about complex solutions?*
this
đđđđđđđ
I have watched your video several times and still do not understand why ABC need be equal.
In the real world, all the quantities of the left may only be positive. If we say
f(x) = 2ËŁ+ (â )ËŁ+ (Ÿ)ËŁ
then f(x) > 0 for all real x.
f'(x) = 2ËŁln 2 + (â )ËŁln â + (Ÿ)ËŁln Ÿ
= 2ËŁln 2 + (â )ËŁ(ln 2- ln 3)+ (Ÿ)ËŁ(ln 3-2 ln 2)
At x = 0, we find
f'(0) = ln 2 + (ln 2- ln 3)+ (ln 3-2 ln 2)
= ln 2 + ln 2- ln 3+ ln 3-2 ln 2
= 0
f(0) = 3
The second derivative at 0 is
(ln 2)ÂČ + (ln â )ÂČ + (ln Ÿ)ÂČ
Since this is positive, the function only increases with positive or negative change in x.
solution
x = 0
Nice!