MHB 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:

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

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

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

In another convention:

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

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:

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

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:

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

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

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

In another convention:

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

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:

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

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