To find log, you need to have log tables. Let us take an example that you have to find log 32.62. This log is to the base 10 always.

Step 1 : Ignore the decimal place in the given number. Hence, view the number as 3262. Now, split it into 2 digit + 1 digit + 1 digit which is 32, 6 and 2.

Step 2:  Find the intersecting number between 32 and 6. Note it down. Row 32 and Column 6 has 5132

Step 3: Find the intersecting number between 32 and 2. It is given as 3 here. Add this to the previous result. So 5132 + 3 = 5135. This is called the Mantissa.

Step 4: We need to find the characteristic which comes before the decimal. Whatever is after the decimal point is the mantissa. Here, ?.5135. So we need to find ? which is characteristic

Step 5: By trial and error method, we need to find characteristic n such that a^c < n and a^c+1 > n. The number we have is 32.62. Let us try c to be 1 first

10¹ < 32.62 and 10² > 32.62 So characteristic is 1 in this case. So number is 1.5135. Hence, log (32.62) = 1.5135

Step 6: Suppose the number is 326.2. Then, 10¹ < 326.2 ; 10² is also < 326.2

            So let us try n = 2, 10² < 326.2 ; 10³ > 326.2 So characteristic is 2 in this case. Hence, log (326.2) = 2.5135

Step 7: On similar lines, log 32.62; This number is between 10¹ and 10² Hence, characteristic is 1. log (32.62) = 1.5135

  log 3.262; This number is between 10⁰ and 10¹ Hence, characteristic is 0. log (3.262) = 0.5135

  log 0.3262; This number is between 10-¹ and 10⁰ Hence, characteristic is -1. log (0.3262) = -1.5135

  log 0.03262; This number is between 10-² and 10^-1 Hence, characteristic is -2. log (0.03262) = -2.5135