SOLUTION: Find the unknown in the equation log3(3^m+1 plus 3^m+2) = log3 972 Im am having trouble getting to the answer which is m = 4 Please note that the 3 in the log 3 972 is sm

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: Find the unknown in the equation log3(3^m+1 plus 3^m+2) = log3 972 Im am having trouble getting to the answer which is m = 4 Please note that the 3 in the log 3 972 is sm      Log On

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Question 133341: Find the unknown in the equation
log3(3^m+1 plus 3^m+2) = log3 972
Im am having trouble getting to the answer which is m = 4
Please note that the 3 in the log 3 972 is small
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C%283%5E%28m%2B1%29%2B3%5E%28m%2B2%29%29%29=+log%283%2C%28972%29%29 Start with the given equation


3%5E%28log%283%2C%283%5E%28m%2B1%29%2B3%5E%28m%2B2%29%29%29%29=+3%5E%28log%283%2C%28972%29%29%29 Raise both sides as exponents with bases of 3. This will eliminate the logs


3%5E%28m%2B1%29%2B3%5E%28m%2B2%29=+972 Simplify


3%5E%28m%29%2A3%5E%281%29%2B3%5E%28m%29%2A3%5E%282%29=+972 Break up the left side using the identity x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez


3%5E%28m%29%2A3%2B3%5E%28m%29%2A9=+972 Evaluate 3%5E1 to get 3. Evaluate 3%5E2 to get 9


3%2A3%5E%28m%29%281%2B3%29=+972 Factor out the GCF


3%2A3%5E%28m%29%284%29=+972 Add


3%2A3%5E%28m%29=+243 Divide both sides by 4


3%5E%28m%29=+81 Divide both sides by 3


3%5E%28m%29=+3%5E4 Rewrite 81 as 3%5E4


Since the bases are equal, this means that the exponents are equal. So m=4


So our answer is m=4