What is the difference between ln 4 and log 4?

[mathdad]

I am reviewing Calculus 1 integration learned long ago in the 1990s.

Integrate (1/x) dx from 1 to 4.

The textbook answer is ln 4.

However, many of my friends tell me that the answer can also be written as log 4.

But, ln 4 does NOT equal log 4.

In fact, ln 4 > log 4.

Who is right? Why?

 

[MarkFL]

It depends on what shorthand notation one uses for $\log_e(x)$.

 

[mathdad]

It depends on what shorthand notation one uses for $\log_e(x)$.

The integral of (1/x) is ln x.

From 1 to 4:

ln 4 - ln 1

ln 4 - 0

Answer: ln 4

However, my friend said the following:

log 4 - log 1

log 4 - 0

log 4

Who is right?

 

[topsquark]

I'll expand a bit beyond MarkFL's comment. You problem is a matter of notation, not a conceptual one.

In many sources we have that \(\displaystyle ln(x) = log_e(x)\). Sometimes you will see \(\displaystyle log_e(x) = log(x)\). In fact some also say that \(\displaystyle log_{10}(x) = log(x)\).

In your case we need the \(\displaystyle ln(4) = log_e(x)\).

-Dan