Why ln for natural log

This relationship makes sense when you think in terms of time to grow. The net effect is the same, so the net time should be the same too and it is. How about division? In general we have. I hope the strange math of logarithms is starting to make sense: multiplication of growth becomes addition of time, division of growth becomes subtraction of time. We can consider the equation to be:.

If I double the rate of growth, I halve the time needed. Cool, eh? The natural log can be used with any interest rate or time as long as their product is the same. You can wiggle the variables all you want. The Rule of 72 is a mental math shortcut to estimate the time needed to double your money. Uh oh. It takes. However, Which is another useful rule of thumb. The Rule of 72 is useful for interest rates, population growth, bacteria cultures, and anything that grows exponentially.

I hope the natural log makes more sense — it tells you the time needed for any amount of exponential growth. Learn Right, Not Rote. Home Articles Popular Calculus. Our new student and parent forum, at ExpertHub. See how other students and parents are navigating high school, college, and the college admissions process.

Ask questions; get answers. How to Get a Perfect , by a Perfect Scorer. Score on SAT Math. Score on SAT Reading. Score on SAT Writing. What ACT target score should you be aiming for? How to Get a Perfect 4. How to Write an Amazing College Essay. A Comprehensive Guide. Choose Your Test. 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. My two theories about this are. According to Earliest Uses of Function Symbols :. 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. Ask Question. Asked 6 years, 2 months ago. Active 1 year, 9 months ago. Viewed 2k times.

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