SOLUTION: log (subscript 2) 48 - 1/3 log (subscript 2) 27

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Question 196669: log (subscript 2) 48 - 1/3 log (subscript 2) 27
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C%2848%29%29-%281%2F3%29log%282%2C%2827%29%29 Start with the given expression.


log%282%2C%2848%29%29-log%282%2C%2827%5E%281%2F3%29%29%29 Rewrite the second log using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


log%282%2C%2848%29%29-log%282%2C%28root%283%2C27%29%29%29 Convert to radical form.


log%282%2C%2848%29%29-log%282%2C%283%29%29 Evaluate the cube root of 27 to get 3


log%282%2C%2848%2F3%29%29 Combine the logs using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29


log%282%2C%2816%29%29 Reduce


log%282%2C%282%5E4%29%29 Rewrite 16 as 2%5E4


4%2Alog%282%2C%282%29%29 Pull down the exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


4%2A1 Evaluate the log base 2 of 2 to get 1


4 Multiply


So log%282%2C%2848%29%29-%281%2F3%29log%282%2C%2827%29%29=4