What is the difference between log and ln?

[mathdad]

In simple words, what is the difference between log and ln?

 

[MarkFL]

In one notational convention:

\(\displaystyle \ln(x)=\log_{e}(x)\)

\(\displaystyle \log(x)=\log_{10}(x)\)

This is typically what you see in pre-calculus and elementary calculus courses.

In another convention:

\(\displaystyle \log(x)=\log_{e}(x)\)

This is what you'll find at W|A (but it will recognize ln as well). When you get into analysis, this is what you'll likely find used there.

In computer science, you may see:

\(\displaystyle \log(x)=\log_{2}(x)\)

So, it really depends on the context...and the notation "log" often means the most commonly used base in that particular environment.

 

[mathdad]

In one notational convention:

\(\displaystyle \ln(x)=\log_{e}(x)\)

\(\displaystyle \log(x)=\log_{10}(x)\)

This is typically what you see in pre-calculus and elementary calculus courses.

In another convention:

\(\displaystyle \log(x)=\log_{e}(x)\)

This is what you'll find at W|A (but it will recognize ln as well). When you get into analysis, this is what you'll likely find used there.

In computer science, you may see:

\(\displaystyle \log(x)=\log_{2}(x)\)

So, it really depends on the context...and the notation "log" often means the most commonly used base in that particular environment.

Good information.

 

[HOI]

The reason why "\(\displaystyle \log(x)= \ln(x)\)" in higher courses (calculus and beyond) and "\(\displaystyle \log_{10}(x)\)" is just dropped is that \(\displaystyle \ln(x)\) satisfies the simple differentiation rule \(\displaystyle \frac{d\ln(x)}{dx}= \frac{1}{x}\) while if the base is 10, \(\displaystyle \frac{d \log_{10}(x)}{dx}= \frac{1}{\ln(10)x}\).