Question

Given In 3= 1.0986 and In 4 = 1.3863, find the value of the following logarithm without using a calculator. In 36 In 365

Answer 1

36 = 3 * 3 * 4 = 3^2 * 4

so,

ln 36 = ln (3^2 * 4) = ln3^2 + ln 4 = 2 ln3 + ln4 = 2 * 1.0986 + 1.3863 =

= 2.1972 + 1.3863 = 3.5835

Note:

we have used the following rule of ln

ln(a*b) = ln a + ln b

ln(a^b) = b * ln a