SOLUTION: if, log2=a and log3=b, express log cuberoot972 in terms of a and b. the answer is 2a+5b over 3. please help.

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: if, log2=a and log3=b, express log cuberoot972 in terms of a and b. the answer is 2a+5b over 3. please help.       Log On

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Question 35499: if, log2=a and log3=b, express log cuberoot972 in terms of a and b. the answer is 2a+5b over 3. please help.
Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
First, factor 972 into prime factors.
972+=+9%2A108+=+9%2A+9+%2A12=+3%5E2%2A3%5E2%2A3%2A4+=+3%5E5%2A2%5E2

Now, log+%28root%283%2C972%29%29
log+%28972%5E%281%2F3%29%29

%281%2F3%29%2A+log+972

%281%2F3%29+%2A+log+%283%5E5%2A2%5E2%29+

+%281%2F3%29%2A+%28log+%283%5E5%29+%2B+log+%282%5E2%29+%29+

+%281%2F3%29+%2A+%285+log+3+%2B+2+log+2%29+

+%285+log+3+%2B+2+log+2%29%2F3

+%285b%2B+2a%29+%2F3+

R^2 at SCC