How is ln related to e

It appears in many applications. The exponential function arises whenever a quantity grows or decays at a rate proportional to its current value. Key Terms tangent : A straight line touching a curve at a single point without crossing it. Learning Objectives Identify some properties and uses of the natural logarithm. Key Takeaways Key Points The natural logarithm is the logarithm with base equal to e.

The number e and the natural logarithm have many applications in calculus, number theory, differential equations, complex numbers, compound interest, and more. Key Terms natural logarithm : The logarithm in base e. Licenses and Attributions.

In other words, the logarithm gives the exponent as the output if you give it the exponentiation result as the input. Using base 10 is fairly common. In that case, it's good to ask. We can use the product rule for exponentiation to derive a corresponding product rule for logarithms. See how other students and parents are navigating high school, college, and the college admissions process.

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What Is ln? The 4 Key Natural Log Rules There are four main rules you need to know when working with natural logs, and you'll see each of them again and again in your math problems. Natural Log Sample Problems Now it's time to put your skills to the test and ensure you understand the ln rules by applying them to example problems. Next, we use the power rule to get: 2ln 7 -ln 5. What's Next? Have friends who also need help with test prep? Share this article! Christine Sarikas. About the Author.