maths question help
 
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maths question help


Hassan
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part b 

thanks 

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Further_Maths_Student
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f(x) = 2 + ln(x + 3)

f^2(x) = 2 + ln(2 + ln(x + 3) + 3)

= 2 + ln(ln(x + 3) + 5)

Now plug x = e^N - 3

so f^2(e^N - 3) = 2 + ln(ln(e^N -3 + 3) + 5)

Now you can equate this to ln(53e^2)

so f^2(e^N - 3) = 2 + ln(ln(e^N) + 5) = ln(53e^2)

Spoiler
Solution from here

And I would turn '2' into ln(e^2) so that you have an equation that has ln(left hand side) = ln(right hand side) so then you can do LHS = RHS and solve it.

ln(e^2) + ln(ln(e^N) + 5) = ln(53e^2)

ln(e^2(ln(e^N) + 5)) = ln(53e^2)

Now cancel out ln's from both sides

e^2(ln(e^N) + 5) = 53e^2

e^2(N + 5) = 53e^2

N + 5 = 53

N = 48

 

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Hassan
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@further_maths_student 

thanks i get it now

for f^2 functions i thought you just square the f function, not substitute the f into f function. How do you know when to just square it or when to see it as a composite function?

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Further_Maths_Student
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@hassan 

f^2(x) always represents composite function ff(x)

(f(x))^2 would be square of the function. Although, I don't see the square of a function that often

 

Kind of like how

\frac{d^{2}y}{dx^2}

is different to

(\frac{dy}{dx})^2

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Hassan
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