SOLUTION: If log2=a and log3=b, write an expression in terms of a and b that is equivalent to log 9/20.

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Question 731192: If log2=a and log3=b, write an expression in terms of a and b that is equivalent to log 9/20.
Found 2 solutions by fcabanski, lwsshak3:
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
log (x/y) = log(x) - log(y)

log(x*y) = log(x)+log(y)

log(x^y) = y*log(x)

log(10) = 1. Log is log base 10. And log base n of n = 1.


Use those log properties to solve this problem.


log(9/20) = log(9) - log(20) = log(3^2) - log(2*10) = 2*log(3) - (log(2) +log(10)) = 2b - (a+1) = 2b-a-1

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)


Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If log2=a and log3=b, write an expression in terms of a and b that is equivalent to log 9/20.
log 9/20=log(9)-log(20)
=log(3^2)-log(10*2)
=2log(3)-[(log(10)+log(2)]
=2b-(1+a)
=2b-1-a