The notation is used in physics and engineering to denote the natural logarithm while mathematicians commonly use the notation in this work denotes a natural logarithm whereas denotes the common logarithm there are a number of notational conventions in common use for indication of a power of a natural logarithm while some authors use i e.

The natural logarithm whose symbol is ln is a useful tool in algebra and calculus to simplify complicated problems in order to use the natural log you will need to understand what ln is what the rules for using ln are and the useful properties of.

The natural logarithm often abbreviated ln is the inverse of the exponential function it is often used in mathematics for calculations involving time and growth rates in python several libraries allow us to compute it like the math library and the numpy library.

The decimal expansion of the natural logarithm of 2 is given by ln2 0 69314718055994530941 oeis a002162 it was computed to 10 11 decimal digits by s kondo on may 14 2011 yee the earls sequence starting position of n copies of the digit n for ln2 is given for n 1 2 by 4 419 2114 3929 38451 716837 6180096 10680693.

In the natural logarithm the base e is the same number as in the natural exponential logarithm that we saw in the last section here is a sketch of both of these logarithms from this graph we can get a couple of very nice properties about the natural logarithm that we will use many times in this and later calculus courses begin array l.

Note the logarithm to base e is a very important logarithm you will meet it first in natural logs base e and will see it throughout the calculus chapters later 3 determine the exact value of log 3root 4 27 answer.