Logarithms are the functions which are written as numbers which consist a base for that number to produce a
real number. Natural logarithms are logarithms of a number with a fixed base, ‘e’. Natural logarithms are
generally expressed as ‘lnx’ or ‘logex’. Natural log calculator is the fun tool which can give the natural log
value of any number.
Example 1: Evaluate the value of the natural log of the expression ln(18) given ln(2)= 0.693 and
ln(3)= 1.098.
Given -> ln(2)= 0.693 and ln(3)= 1.098
In order to find the value of ln(18), we have to split into pieces.
ln(18) = ln(2 * 9)
Applying the rule-> ln(a * b) = ln(a) + ln(b)
ln(2 * 9) = ln(2) + ln(9)-> ln(2) + ln(32)
Applying the rule-> ln(am) = m * ln(a)
ln(2) + ln(9) = ln(2) + 2ln(3)
ln(18) = 0.693 + (2 * 1.098)
l(18)= 2.889
Example 2: Solve for ‘x’ the given natural log equation: ln(x + 15) = 3
Given equation: ln(x + 15) = 3
The above equation contains the natural logarithm; hence its base is ‘e’.
Applying the formula -> lne(a) = x -> a = ex
Hence -> (x + 15) = e3
The value of e3 = 20.085
Hence x + 15 = 20.085
Now subtract 15 on both sides -> x + 15 – 15 = 20.085 – 15-> 5.085
Hence the value of ‘x’ = 5.085