What is the difference between logarithm and natural logarithm

That's why base 10 was used: to make that possible. And so on. Has someone posted that question here? Will it be on the test? Next time someone does that, I'm going to say "Who cares? Natural base e makes this slope equal to 1. The number is called e after Leonhard Euler, a mathematician that first gave this number a meaning and found its value. Euler worked on a formula for compounding interest.

It is approximately 2. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. I was told that it's basically the same thing and can be used interchangeably, but if it's the same, what is the point of having another one? To reword it, if log and ln is the same, why use ln over log and vice versa?

They are not the same!! They are both logarithms, but they are different logarithms. The question you're asking here is to what power do I need to raise a to get b?

This exact thing can be said using logarithms as shown below :. That value a there is what we call our base , and it can vary based on what problem you're trying to solve. Find log 7 Use the Change of Base formula. You can use common logarithms or natural logarithms. Use the calculator to evaluate the quotient. If you had used natural logarithms, you would have gotten the same answer:. Find log 3 Find log 5 The correct answer is 3.

When using the change of base formula, the log of the original base is the denominator:. You found the value of log Common logarithms base 10, written log x without a base and natural logarithms base e , written ln x are used often. Scientific and graphing calculators have keys or menu items that allow you to easily find log x and ln x , as well as 10 x and e x.

Using these keys and the change of base formula, you can find logarithms in any base. Example Problem Find e 1. Answer 4. Example Problem Find 10 1. Answer Example Problem Find ln 3, using a calculator.

Answer 1. Example Problem Find log 34, using a calculator. C D 10,, Incorrect. Plot the points. Answer Connect the points as best you can, using a smooth curve not a series of straight lines. B Incorrect. C Correct. D Incorrect. Example Problem Find log 7 Example Problem Find log 3 In These graphs will show you the difference between log and ln graph. To solve logarithmic problems,one must know the difference between log and natural log.

Having a key understanding of the exponential functions can also prove helpful in understanding different concepts. Some of the important difference between Log and natural log are given below in a tabular form:. Log generally refers to a logarithm to the base Ln basically refers to a logarithm to the base e.

This is also known as a common logarithm. This is also known as a natural logarithm. The common log can be represented as log10 x. The natural log can be represented as loge x. The log function is more widely used in physics when compared to ln. As logarithms are usually taken to the base in physics, ln is used much less. Mathematically, it can be represented as log base