Logarithms - What is e? | Euler's Number Explained | Infinity Learn NEET

TL;DR

'e' is a mathematical constant that represents the maximum possible result after continuously compounding a 100% growth over one time period.

Transcript

What is ‘e ’? The two most common logarithms used are log to the base 10 and log to the base e. Why are they the most commonly used logarithms? How do we really understand them? Log to the base 10 is kind of intuitive. It’s easier to talk in multiples of 10. Ten, one hundred, one thousand and so on… And log to the base ten gives us an easier scale ... Read More

Key Insights

• ⚾ Logarithms to the base 10 are intuitive and easier to work with, while logarithms to the base e represent natural logarithms.
• ⌛ 'e' represents the maximum possible result after continuously compounding a 100% growth over one time period.
• 🙈 Growth in nature is continuous and gradual, unlike the discrete growth seen with doubling.
• 🤚 The formula for calculating growth with different time periods is 1 plus '1 over n', the whole raised to n.
• 😥 'e' is an irrational number, approximately equal to 2.718, with infinite digits after the decimal point.
• ☠️ Continuous compounding of a 100% growth results in a maximum growth rate of approximately 171.8%.
• ☠️ 'e' can be used to calculate growth with different growth rates and time periods.

Questions & Answers

Q: What is the difference between logarithms to the base 10 and base e?

Logarithms to the base 10 are intuitive and easier to work with, while logarithms to the base e represent natural logarithms and can be written as LN.

Q: How is growth related to doubling and a 100% increase?

Doubling the value is equivalent to a 100% increase, and growth can be represented as 2 raised to x or 1 plus 100% raised to x.

Q: How does growth occur in nature?

Growth in nature is gradual and continuous, unlike the discrete growth seen in doubling. It happens gradually over time.

Q: What is the formula for calculating growth with different time periods?

The formula is 1 plus '1 over n', the whole raised to n, where n represents the number of time periods.

Summary & Key Takeaways

• Logarithms to the base 10 and base e are commonly used, with base 10 being intuitive and easier to work with.

• Understanding 'e' requires understanding gradual growth and compounding.

• 'e' is approximately 2.718 and represents the maximum result after continuously compounding a 100% growth over one time period.