How to use Log tables ?

Let us take one example; let us find the log(345.687) value. For most of the numerical calculations, the base will be 10. 

We need to express the given number with only one digit before the decimal point, see below.

345.687=3.456×10^(2)

Now, the power of 10, i.e., 2 is our characteristic value, for the given number. Now, we need to look up the log table with the four digits 3456. Take the first two digits i.e., search for 34 in the log table, in that row, note the number in the column corresponding to 5, (= 5378). Now, in the same row, look at the mean difference value under column 6, (= 8). Add these two, i.e., 5378 + 8 = 5386. 

Now, place the characteristic value before this, i.e., 25386, and place the decimal point after one digit, i.e., = 2.5386. This is the value of log(345.687) =2.5386.

Let us look at a couple more examples below, which makes it clearer.

	Characteristic value	look-up Log-table	Mean difference	Total value
log(4567.453) = ?	= 4.567×10^3 → 3	45th row, under column 6 = 6590	Same row, under col 7 in mean diff. = 7.	6590 + 7 = 6597. Place characteristic value => 36597.  Place the decimal point => 3.6597
log(0.9668) = ? = log( 9.668 x 10^(-1) ) = log(9.668) -1.	= 9.668×10^0 → 0	96th row, under column 6 = 9850	Same row, under col 8 in mean diff. = 4.	9850 + 4 = 9854. Place characteristic value => 09854. Place the decimal point => 0.9854. Now, the final value = 0.9854 – 1 =   = - 0.0146. (yes, that is negative !)