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# C3 logs and exponentials

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1. What's so special about ???

I cant remember but my teacher said something about the gradient equalling the same y value n the y axis or something... o.o
2. (Original post by bigdonger)

I cant remember but my teacher said something about the gradient equalling the same y value n the y axis or something... o.o
Do ln of both sides you get lny = x
3. Differentiate or integrate y with respect to x and you get e^x again.
4. (Original post by bigdonger)

I cant remember but my teacher said something about the gradient equalling the same y value n the y axis or something... o.o
The gradient of y = e^x is equal to e^x.
When you differentiate y = e^x you get dy/dx = e^x... This is not true for y = e^2x (or any other function of x), however. You will learn this once you cover the differentiation chapter in C3
5. (Original post by Reda2)
Do ln of both sides you get lny = x
ok... so what does that mean? ...
oh i see ok but is that's all that's special about y=e^x?
(Original post by Wunderbarr)
Differentiate or integrate y with respect to x and you get e^x again.
yup teacher told me that
(Original post by JLegion)
The gradient of y = e^x is equal to e^x.
When you differentiate y = e^x you get dy/dx = e^x... This is not true for y = e^2x, however. You will learn this once you cover the differentiation chapter in C3
oh? is there proof for this? how does one know?
6. (Original post by bigdonger)
oh? is there proof for this? how does one know?
You will learn this in the C3 differentiation chapter.

I believe the proof for this is beyond the A-Level syllabus
7. (Original post by bigdonger)
ok... so what does that mean? ...
oh i see ok but is that's all that's special about y=e^x?

yup teacher told me that

oh? is there proof for this? how does one know?
y = e^x
lny = lne^x
lny = x
(Implicit diff wrt x)
(1/y)(dy/dx) = 1
dy/dx = y
dy/dx = e^x

8. (Original post by JLegion)
You will learn this in the C3 differentiation chapter.

I believe the proof for this is beyond the A-Level syllabus
ah ok
(Original post by XOR_)
y = e^x
lny = lne^x
lny = x
(Implicit diff wrt x)
(1/y)(dy/dx) = 1
dy/dx = y
dy/dx = e^x

probably need to earn that bit, i understand the rest though.....
9. e is a special number because it is the base of the natural logarithm. It is a special number and comes up a lot in growth and decay. It is defined in many ways but I think the most natural way is that it can be defined as
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