# What are common mistakes students make with base e?

Jan 25, 2017

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

$\log x = {\log}_{e} \frac{x}{\log} _ 10 e = \ln \frac{x}{\log} e$.

So,

$\left(\log x\right) ' = \frac{1}{\log} e \left(\ln x\right) ' = \frac{1}{\log} e \left(\frac{1}{x}\right)$