Question

What are common mistakes students make with base e?

Answer 1

see explanation

Explanation:

It is called the natural logarithm for the transcendental base e.

Any value of e used in computation , like e = 2.718, is an

approximation only.

Like the value of `pi`, the value cannot be expressed, in

mathematical exactitude

The notation ln x is exclusive for this logarithm, in contrast to log x

notation for base-10 logarithm.

In differentiation,

(ln x)'= 1/x. So, it is wrong to write (log x)'=1/x.

The conversion formula is

`log x = log_e x/log_10 e= ln x/loge`.

So,

`(log x)'=1/loge(ln x)'= 1/log e(1/x)`