MYTUTOR SUBJECT ANSWERS

344 views

Which Real values of x satisfy 3/ln(x) = ln(x) + 2?

The problem with this equation lies with the denominator on the left hand side. If we recall our graph of ln(x) however, we know that ln(x) is always positive and not equal to 0. Now we can safely multiply it up. The equation now reads:

3 = (ln(x))2 + 2ln(x)

We can recognise this as a quadratic equation in ln(x), and factorise it as such:

(ln(x)+3)(ln(x)-1) = 0

from which we deduce the solutions exist where ln(x) is equal to 1 or -3, the latter of which does not exist for any real values. Hence we consider ln(x) = 1, which is achieved when x = e, our one and only real solution. 

(note that we can confirm this solution by substituting x = e into the original equation).

Mark H. GCSE Maths tutor, A Level Maths tutor

10 months ago

Answered by Mark, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

423 SUBJECT SPECIALISTS

£20 /hr

Vlad B.

Degree: Mathematics (Masters) - Bath University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Hi! I am studying Mathematics at Bath University and I am passionate about teaching, and learning mathematics.”

MyTutor guarantee

|  1 completed tutorial

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

£26 /hr

Luke B.

Degree: Mathematics (Masters) - Sheffield University

Subjects offered:Maths, Further Mathematics + 3 more

Maths
Further Mathematics
.STEP.
.MAT.
-Personal Statements-

“I am a fun, engaging and qualified tutor. I'd love to help you with whatever you need, giving you the support you need to be the best you can be!”

About the author

Mark H.

Currently unavailable: for new students

Degree: Mathematics (Bachelors) - Nottingham University

Subjects offered:Maths

Maths

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Posts by Mark

Where z is a complex number, what is the cartesian form of |Z-2+3i| = 1?

Which Real values of x satisfy 3/ln(x) = ln(x) + 2?

Other A Level Maths questions

Why bother with learning calculus?

How can we solve a two-equation, two-unknown values?

What is the integral of x^2 + 3x + 7?

How do you derive the quadratic formula?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok