Logarithm using table

• Finding logarithm of a value using table is just combining the values of characteristic and mantissa

Example#1

Find the value of $\log(678.467)$

Solution:

• First find characteristic

  $678.467$

  $6.78467\times10^{2}$

  $2$ is the value of characteristic

• Find the mantissa of given number

  $678.467$

  $678.5$

  $6785$

• Use log table to find mantissa

  Mantissa of $6785$ is $8312+3=8315$ Mantissa is $0.8315$

• Combine the characteristic and mantissa

  $2.8315$

• The value of $\log(678.467)=2.8315$

Example#2

Find the value of $\log(0.0345)$

Solution:

• First find characteristic

  $0.0345$

  $3.45\times10^{-1}$

  $-1\text{ or }\bar{1}$ is the value of characteristic

• Find the mantissa of given number

  $0.0345$

  $345$

  Here mean difference column value is missing, its fine we won’t search for the value in mean difference columns

• Use log table to find mantissa

  Mantissa of $345$ is $5378$ Mantissa is $0.5378$

• Combine the characteristic and mantissa

  $-1.5378$

• The value of $\log(0.0345)=-1.5378$