MYTUTOR SUBJECT ANSWERS

438 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

295 SUBJECT SPECIALISTS

£20 /hr

Christopher C.

Degree: Physics (Bachelors) - Manchester University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“I am a friendly, patient tutor who is passionate about their subject and enjoys teaching others about it.”

MyTutor guarantee

£20 /hr

Martin B.

Degree: Physics (Masters) - Durham University

Subjects offered:Maths

Maths

“I’m an enthusiastic first year physics student with over 2 years of tutoring experience to help you achieve stellar academic results.”

MyTutor guarantee

£20 /hr

Neal A.

Degree: Mechanical Engineering (Masters) - Manchester University

Subjects offered:Maths

Maths

“I'm a student at the University of Manchester and am willing to help every student get a chance to be successful and excel at school and have a bright future.”

MyTutor guarantee

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

I did all the past papers but I still only achieved a C grade, what am I doing wrong?

For rectangles of area 100 m^2 what is the perimeter of the rectangle with the smallest perimeter?

How do I use the chain rule to differentiate polynomial powers of e?

Differentiate the equation y = x^2 + 3x + 1 with respect to x.

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