maths question help

Notifications
Clear all

# maths question help

Posts: 59
Topic starter
(@hassan)
Trusted Member
Joined: 11 months ago

part b

thanks

4 Replies
Posts: 257
(@further_maths_student)
Reputable Member
Joined: 2 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: 11 months ago

Trusted Member
Posts: 59

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: 2 years ago

Reputable Member
Posts: 257

$f^2(x)$ 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: 11 months ago

Trusted Member
Posts: 59

## How To Choose The Right University For You?

Choosing the right university is one of the most important decisions you will make in your life. For most students,...
View Post

## 2022 Real Exams Cancelled Again?

Ofqual and the government have announced that they are in talks about the changes for the 2022 examinations (GCSE, AS-Level...
View Post

## Should I do a Physics Degree?

A physics degree will be a good choice for you if you enjoy studying A-Level Maths and Physics. The degree...
View Post

## How To Deal With Rejection (From University)?

No matter what anyone says, rejection hurts. A LOT. Rejection is an almost unavoidable experience of being human. We all...
View Post