SOLUTION: a) Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e. In computer science, digital computers are based on the binary numbering system

Question 26557: a) Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he/she needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:

logb a= log a/log b
please solve quickly. thank you
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he/she needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:
logb a= log a/log b
YA IT IS OK SO IF YOU WANT LOG 20 TO BASE 2 THEN FIND LOG 20 TO BASE 10 AND DIVIDE IT WITH LOG 2 TO BASE 10....OR....THEN FIND LOG 20 TO BASE E AND DIVIDE IT WITH LOG 2 TO BASE E.
OK..WHAT ELSE DO YOU WANT TO KNOW
please solve quickly.
WHAT IS TO BE SOLVED?YOU WANT PROOF OF THE ABOVE THEOREM ?..PLEASE CLARIFY..
PROOF......
LET LOG A TO BASE B BE EQUAL TO X
SO B^X=A..............I
LET LOG A TO A STANDARD BASE SAY 10 BE EQUAL TO Y.SO
10^Y=A............II
LET LOG B TO THE SAME STANDARD BASE 10 BE EQUAL TO Z.SO
10^Z=B.............III,SUBSTITUTING II AND III IN I...
{(10^Z)^X}= 10^Y
10^(Z*X)= 10^Y
ZX=Y
X=Y/Z...HENCE
logb a= log a/log b

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