Part 2/5:
The natural logarithm is defined with the base ( e ), a mathematical constant approximately equal to 2.718. If we have the function ( y = e^x ), the natural logarithm is its inverse, represented as:
[
y = \ln(x)
]
In most mathematical discourse, this is often abbreviated simply as "ln" rather than writing it out as ( \log_e(x) ).
Logarithm Base 10
The logarithm with base 10 is commonly denoted ( \log_{10}(x) ) or simply ( \log(x) ) in many mathematical texts. This notation implies:
[
y = \log_{10}(x) \implies x = 10^y
]
This logarithm appears frequently in science and engineering due to its ease of use in calculations.