SOLUTION: If ((log_3)2) = x, simplify : Log_3 (6(square root 2))

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Question 174793: If ((log_3)2) = x, simplify :
Log_3 (6(square root 2))
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C%286%2Asqrt%282%29%29%29 Start with the given expression.


log%283%2C%286%29%29%2Blog%283%2C%28sqrt%282%29%29%29 Break up the log using the identity log%28b%2C%28A%2AB%29%29=log%28b%2C%28A%29%29%2Alog%28b%2C%28B%29%29


log%283%2C%286%29%29%2Blog%283%2C%28%282%29%5E%281%2F2%29%29%29 Convert from radical to exponential notation.


log%283%2C%286%29%29%2B%281%2F2%29log%283%2C%282%29%29 Rewrite the second log using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


log%283%2C%286%29%29%2B%281%2F2%29x Replace log%283%2C%282%29%29 with "x"


So log%283%2C%286%2Asqrt%282%29%29%29 simplifies to log%283%2C%286%29%29%2B%281%2F2%29x where x=log%283%2C%282%29%29