Question
Thu February 09, 2012 By: Venkat Rao
 

how cn v calculate log of any number?

Expert Reply
Thu February 09, 2012
 log of numbers of the common (base 10) logarithm are “powers of ten.” The log of 10 is 1; it is not multiplied by anything. It is the base. But 100, which is 10 x 10, is written as 102 and the log of 100 is 2. Log 1,000 is 3, 10,000 is 4, and so on. On multiples of 10, count the zeroes and you know the logarithm of the number. But what about other numbers? If I ask my spreadsheet or calculator for the log of 2, the answer will be 0.30103. Put another way, it means that 2, expressed as a power of 10, is that fraction, and that 10.30103 equals 2 .
• The log of 5 is obtained by dividing 10 by 2, thus 1 - .30103 = .69897.
• The log of 4 is easy too, 2 x 2, thus .3013 + .3013 = .60206.
• The log of 8 is 4 x 2, therefore .30103 + .60206 = .90309.
• The log of 20? . 2 x 10 = .30103 + 1 = 1.30103.
• The log of 40? It is 1.60206.
• And 400? It is 2.60206.  100 x 4, 2 + .60206.
Prime numbers divisible only by 1 and themselves require the long process. 3 and 7 require slow calculation. But after that it is easy to calculate the log of 6, 9, 12, 14, 60, 70, 90, and so on .
Related Questions
Mon September 05, 2016

.?

Mon September 05, 2016

Root E^ root X, X>0.??

Ask the Expert