SOLUTION: Log6 54 + log6 4 =

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Question 1084208: Log6 54 + log6 4 =
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Log Rules:
Let b be the base of the logarithm. The base must positive, so b > 0. Also we can't let b = 1 be possible so the restriction is that b+%3C%3E1. For any positive x,y values, we can say
  1. log%28b%2C%28x%29%29%2Blog%28b%2C%28y%29%29=log%28b%2C%28x%2Ay%29%29
  2. log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29
  3. log%28b%2C%28b%29%29=1
We'll use these log rules below
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log%286%2C%2854%29%29%2Blog%286%2C%284%29%29=log%286%2C%2854%2A4%29%29 Using log rule 1
log%286%2C%2854%29%29%2Blog%286%2C%284%29%29=log%286%2C%28216%29%29
log%286%2C%2854%29%29%2Blog%286%2C%284%29%29=log%286%2C%286%5E3%29%29
log%286%2C%2854%29%29%2Blog%286%2C%284%29%29=3%2Alog%286%2C%286%29%29 Using log rule 2
log%286%2C%2854%29%29%2Blog%286%2C%284%29%29=3%2A1 Using log rule 3
log%286%2C%2854%29%29%2Blog%286%2C%284%29%29=3