SOLUTION: use log 3 = 0.477 and log 5= 0.699 to evaluate log 5/3

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Question 420784: use log 3 = 0.477 and log 5= 0.699 to evaluate log 5/3
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
In order to use log(3) and log(5) to find log(5/3) you have to express log(5/3) in terms of log(3) and/or log(5).

Fortunately a property of logarithms, log%28a%2C+%28p%2Fq%29%29+=+log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29, shows us how to express the log of a quotient in terns of the logs of its numerator and denominator. Using this property on log(5/3) we get:
log(5) - log(3)
Now we can replace these logs with the values you were given:
0.699 - 0.477
which simplifies to:
0.222
So log(5/3) = 0.222