SOLUTION: If log2=a and log3=b, express log200 in terms of a and b.

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Question 287937: If log2=a and log3=b, express log200 in terms of a and b.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
You are given expressions to use for log(2) and log(3). And you should know that log(10) = 1 by definition. So your task is to express log(200) in terms of these three.

There are three properties we can use:
  • The log of a product: log%28a%2C+%28p%2Aq%29%29+=+log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29
  • The log of a quotient: log%28a%2C+%28p%2Fq%29%29+=+log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29
    • The log of an exponentiated expression: log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29

So with these properties, if we can express 200 as a product, quotient and/or power of 2's, 3's and/or 10's we will have able to solve the problem. With the 0's at the end of 200 I hope you can see that a product of 10's in involved and with the 2 in front we can see that a 2 is involved:
log(200) = log(2*10*20) = log(2) + log(10) + log(10) = a + 1 + 1 = a + 2