MYTUTOR SUBJECT ANSWERS

595 views

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

307 SUBJECT SPECIALISTS

£36 /hr

Venetia L.

Degree: General Engineering (Masters) - Durham University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I study General Engineering at the University of Durham. I have always enjoyed maths and sciences, so hope to help students who share my love for them too!”

£24 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£30 /hr

Alex S.

Degree: Physics (Bachelors) - Oxford, St Peter's College University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
.PAT.

“Studying Physics at the University of Oxford. Looking to tutor maths and physics at all levels, be sure to send me a message if you have any questions!”

About the author

Eden H.

Currently unavailable: for regular students

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

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
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

What is the equation of the normal line to the curve y = 3x^3 - 6x^2 at the point (1, 4)?

Use integration by parts to find the integral of sin(x)*exp(x)

Why do I have to add +c when I integrate?

Rationalise the denominator of 25/sqrt(5)

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