Notifications

Clear all

maths question help

Last Post

Posts: 59

Hassan

Topic starter

Dec 30, 2021 2:02 pm

(@hassan)

Trusted Member

Joined: 1 year ago

part b

thanks

4 Replies

Posts: 275

Further_Maths_Student

Dec 30, 2021 2:17 pm

(@further_maths_student)

Reputable Member

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

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

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

$N + 5 = 53$

$N = 48$

Reply

Hassan

(@hassan)

Joined: 1 year ago

Trusted Member

Posts: 59

Dec 30, 2021 3:11 pm

Further_Maths_Student

@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?

Reply

Further_Maths_Student

(@further_maths_student)

Joined: 3 years ago

Reputable Member

Posts: 275

Dec 30, 2021 4:48 pm

$f^2(x)$ 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

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

Reply

Hassan

(@hassan)

Joined: 1 year ago

Trusted Member

Posts: 59

Dec 30, 2021 5:16 pm

Further_Maths_Student

@further_maths_student

thanks

Reply

EXAM TOPICS TO COME UP – 2022 SUMMER EXAMS (GCSE and A-Level)

As you know, the topics for GCSE and A-Level exams have been released today by all exam boards. Below are...

View Post

How To Choose The Right University For You?

How To Choose The Right University For You?

Education Studying University

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?

2022 Real Exams Cancelled Again?

A levels Education GCSEs

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?

Should I do a Physics Degree?

Degrees University

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

View Post