SOLUTION: Could you please let me know the difference between "logarithm of a product" and a "Product of logarithms" with examples, if you don't mind. Thank you so much. Andre

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Could you please let me know the difference between "logarithm of a product" and a "Product of logarithms" with examples, if you don't mind. Thank you so much. Andre      Log On


   

Question 28793: Could you please let me know the difference between "logarithm of a product" and a "Product of logarithms" with examples, if you don't mind. Thank you so much. Andre
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
LOG (1000)= 3 SINCE 10^3=1000...THIS CAN ALSO BE OBTAINED AS
LOG(1000)=LOG(10*100)=LOG(10)+LOG(100)=1+2=3 SINCE 10^1=10 AND 10^2=100
IN GENERAL BY USING Z FOR 1000 ,X FOR 10 AND Y FOR 100, WE COCLUDE THAT
LOG(Z)=LOG(X*Y)=LOG(X)+LOG(Y)..THIS READ AS LOG OF A PRODUCT (Z HERE ...OF 2 NUMBERS OR MORE) IS EQUAL TO SUM OF THE LOGS OF THE FACTORS.(X & Y HERE..OR MORE..)
BY PRODUCT OF LOGS WE MEAN
LOG(10)*LOG(100)=1*2=2..
THERE IS NO FORMULA FOR THIS.YOU HAVE TO FIND THE LOGS SEPERATELY AND MULTIPLY.