Logarithm
Euler's number ｅ
The Euler's number ｅ actually came from the Compound Interest, for calculating the loan, the interest of money you borrowed.
We’ve known about e as a constant number as π is. But where does it come from? Here it is:
Btw, you need to learn Calculus to understand this idea. It just simply means the Loan rate approaching to a number but never achieve.
Refer to the lecture from Khan academy for Calculus course: 𝑒 and compound interest
Refer to the lecture from Khan academy for Calculus course: 𝑒 as a limit
When you’re counting how much do you need to pay the loan depends on how often (n) you will repay it, e.g. you will repay the loan "once a year", or "once a month", or "once a day".
The rate WILL NOT going to boost to infinite but only approaching to 2.72 but always less than it.
The larger n is, the closer it is to 2.72.
Natural Log (ln)
The natural logarithm of a number is its logarithm to the base of the math constant 𝗲.
Common Log ((log₁₀𝒙)
The common logarithm is the logarithm with base 10.
Very useful trick for Inverse Functions
Example 1
Solve:
- We take Natural log of both sides:
Example 2
Solve:
- We let both sides to be the power of
e:
Log Rules & Properties
Product Rule
Quotient Rule
Power Rule
Change of Base Rule
Other rules
Construct exponential models
Example
