What is the natural logarithm?

The standard rule for integration is: integrate kx^n dx = kx^(n+1)/(n+1). However, if we try and integrate 1/x in this manner we get, x^0/0, i.e. 1/0, which is infinity. However, if we look at a graph of 1/x, then between two points there is clearly a well defined area, so it must be possible to integrate this. The natural logarithm is a function that we use to do this, whereby ln(a) is the integral of 1/x between 1 and a. It is a logarithmic function with base 'e', where e takes the value of about 2.718, and e^x is known as the exponential function; i.e. it increases at an ever increasing rate. The exponential function is the inverse of the natural logarithm function. 

Eden H. A Level Further Mathematics  tutor, GCSE Further Mathematics ...

1 year ago

Answered by Eden, an A Level Maths tutor with MyTutor

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


£20 /hr

Alicia P.

Degree: Maths and Economics (Bachelors) - Leeds University

Subjects offered:Maths, Physics+ 1 more

-Personal Statements-

“Maths and Economics Student from Uni of Leeds. Very friendly with previous experience of working with and teaching younger people.”

MyTutor guarantee

|  3 completed tutorials

PremiumGiulio P. GCSE Maths tutor, A Level Maths tutor, A Level Economics tu...
£36 /hr

Giulio P.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Physics+ 3 more

Further Mathematics

“Exam Time! I can provide a rapid revision class in any maths module which will test your son or daughter in all the fundamentals”

£30 /hr

Piyush S.

Degree: Electronics Engineering (Doctorate) - Imperial College London University

Subjects offered:Maths


“I am an experienced and passionate tutor for Maths and Science (Physics in particular). Throughout my higher education, I have been wondering about how Mathematics acts as a tool to model and simplify the complicated concepts of the P...”

About the author

Eden H.

Currently unavailable: for regular students

Degree: Engineering Science (Masters) - Oxford, Somerville College University

Subjects offered:Maths, Physics+ 1 more

Further Mathematics

“Hi, I'm Eden, a fourth year engineering student at the University of Oxford. When I was taking my GCSEs my Maths teacher showed me how maths is the language we use to describe our reality, and ever since then I've been impassioned to ...”

You may also like...

Posts by Eden

For a cuboid, the longest side is two units more than the shortest side, and the middle length side is one unit longer than the shortest side. The total surface area of the cuboid is 52 units². (a) Construct an equation to calculate the surface area.

The roots of the equation z^3 + 2z^2 +3z - 4 = 0, are a, b and c . Show that a^2 + b^2 +c^2 = -2

What is the natural logarithm?

Other A Level Maths questions

How do I rationalise the denominator of a fraction which consists of surds?

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

What is the integral of sin^2(x)?

Solve 2sec^2(x) = 3 + tan(x) for 0 < x <pi/2

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