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real number. Natural logarithms are logarithms of a number with a fixed base, ‘e’. Natural logarithms are

generally expressed as ‘lnx’ or ‘log

value of any number.

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)

ln(2 * 9) = ln(2) + ln(9)-> ln(2) + ln(3

ln(2) + ln(9) = ln(2) + 2ln(3)

ln(18) = 0.693 + (2 * 1.098)

Given equation: ln(x + 15) = 3

The above equation contains the natural logarithm; hence its base is ‘e’.

Applying the formula ->

Hence -> (x + 15) = e

Hence x + 15 = 20.085

Now subtract 15 on both sides -> x + 15 – 15 = 20.085 – 15-> 5.085