maths question help

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# maths question help Posts: 59
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(@hassan)
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Joined: 1 year ago
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(@further_maths_student)
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Joined: 3 years ago $f(x) = 2 + ln(x + 3)$ $f^2(x) = 2 + ln(2 + ln(x + 3) + 3)$ $= 2 + ln(ln(x + 3) + 5)$

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 $e^2(ln(e^N) + 5) = 53e^2$ $e^2(N + 5) = 53e^2$ $N + 5 = 53$ $N = 48$ (@hassan)
Joined: 1 year ago

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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? (@further_maths_student)
Joined: 3 years ago

Reputable Member
Posts: 275 $f^2(x)$ 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 $(\frac{dy}{dx})^2$ (@hassan)
Joined: 1 year ago

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Posts: 59

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