Jshek
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so it says "there is going to be a value of a for which the gradient of y=a^x is exactly the sames as a^x. known as e"

lets say we had e^2x

that means dy by dx =2e^2x is equal to e^2x which is not equal when a sub in x as 1...

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ghostwalker
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(Original post by Jshek)
so it says "there is going to be a value of a for which the gradient of y=a^x is exactly the sames as a^x. known as e"

lets say we had e^2x

that means dy by dx =2e^2x is equal to e^2x which is not equal when a sub in x as 1...

confused

Your exponent is 2x, not x.

If you put your function into the form a^x, you have y=(e^2)^x and e^2 does not equal e, and doesn't meet your criterion.
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Jshek
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(Original post by ghostwalker)
Your exponent is 2x, not x.

If you put your function into the form a^x, you have y=(e^2)^x and e^2 does not equal e, and doesn't meet your criterion.
i dont understand
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Jshek
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(Original post by Jshek)
i dont understand
it said it should equal in my book
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mqb2766
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(Original post by Jshek)
so it says "there is going to be a value of a for which the gradient of y=a^x is exactly the sames as a^x. known as e"

lets say we had e^2x

that means dy by dx =2e^2x is equal to e^2x which is not equal when a sub in x as 1...

confused
As ghostwalker said
e^(2x) = (e^2)^x
Which is not e^x.

Have you done the derivative
d(a^x)/dx = ln(a)a^x
? If so, this equals a^x when ln(a)=1, so a=e. This agrees with your example as ln(e^2)=2.

It may help to post a pic of the page you're confused about so we can see the context.
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Jshek
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So I read 14.2 and it says there's going to be a valid of a where gradient function is exactly same as original function

So I look at example 3a.... e^4x and its gradient function 4e^4x. I then sub in x=1 but this contradicts the sentence above as they do not equal
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Jshek
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So I read 14.2 and it says there's going to be a valid of a where gradient function is exactly same as original function

So I look at example 3a.... e^4x and its gradient function 4e^4x. I then sub in x=1 but this contradicts the sentence above as they do not equal
Value instead of valid i meant

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mqb2766
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So I read 14.2 and it says there's going to be a valid of a where gradient function is exactly same as original function

So I look at example 3a.... e^4x and its gradient function 4e^4x. I then sub in x=1 but this contradicts the sentence above as they do not equal
To try and simplify things a bit. Imagine e=3 (engineering approximation of the true value 2.718...).
Then
e^(4x) = (e^4)^x ~ 81^x
This is not e^x ~ 3^x. Just plug in x=1,2,3,... Multiplying the exponent "x" by a constant changes the base "e" so the conclusion about the derivative is no longer true.
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