SOLUTION: I'm in Algebra 2 and this is my first year learning Logarithms.. I don't understand how to use the proerties of lag. to evaluate a problem.. example " log3^9 + log3^36 - log3^4

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I'm in Algebra 2 and this is my first year learning Logarithms.. I don't understand how to use the proerties of lag. to evaluate a problem.. example " log3^9 + log3^36 - log3^4      Log On


   



Question 698001: I'm in Algebra 2 and this is my first year learning Logarithms.. I don't understand how to use the proerties of lag. to evaluate a problem..
example " log3^9 + log3^36 - log3^4

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%283%5E9%29+%2B+log%283%5E36%29+-+log%283%5E4%29+
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You need to follow 2 general rules to simplify this
+log%28a%29+%2B+log%28b%29+-+log%28c%29+=+log%28+%28a%2Ab%29%2Fc+%29+
and
+log%28+a%5Eb+%29+=+b%2Alog%28a%29+
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+9%2Alog%283%29+%2B+36%2Alog%283%29+-+4%2Alog%283%29++
+log%283%29+ is a common factor which I can factor out
+log%283%29%2A%28+9+%2B+36+-+4+%29+
+41%2Alog%283%29+
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Note that if the base is not specified, it is assumed that
the base of the log is +10+.
Actually, any base is possible to use here, and +3+ is the best.
+log%283%2C3%5E9%29+%2B+log%283%2C3%5E36%29+-+log%283%2C3%5E4%29+=+9+%2B+36+-+4+
+41+ This matches the answer
+41%2Alog%283%2C3%29+=+41+
Note that +log%28a%2Ca%29+=+1+ always
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The main thing to remember is
" logs are exponents " and you read something like
+log%285%2C11%29+ as: This is the exponent that I raise +5+ to
and the result is +11+.
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+log%282%2C2%29+ says: This is the exponent that I raise +2+ to
in order to get +2+ ( obviously it is +1 ) , so
+log%282%2C2%29+=+1+
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Hope this helps. I have to keep reminding myself how logs
work to keep it straight. Keep going back to the general
rules and it will eventually make sense.
Write exponents out the long way , too
+5%5E7+=+5%2A5%2A5%2A5%2A5%2A5%2A5+
+5%5E7+=+%285%2A5%2A5%29%2A%285%2A5%2A5%29%2A5+
+5%5E7+=+5%5E3%2A5%5E3%2A5%5E1+
+5%5E7+=+5%5E%28+3+%2B+3+%2B+1+%29+
And on and on . . .