SOLUTION: log subscript 8 square root 80 - log subscript 8 square root 5

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Question 196625: log subscript 8 square root 80 - log subscript 8 square root 5
Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
subtracting logs means dividing their arguments

log subscript 8 [(square root 80)/(square root 5)]

log subscript 8 [square root (80/5)]

log subscript 8 [square root (16)]

log subscript 8 (4)

4 is 2^2 and 8 is 2^3 ___ so 4 = 8^(2/3)

log subscript 8 (4) = 2/3

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... Start with the given expression.


... 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.


... Factor 80 into 16*5.


... Break up the square root.


... Take the square root of 16 to get 4.


... Reduce


... Use the change of base formula



Remember the change of base formula is log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29



... Rewrite each argument as a power of 2


... Pull down the exponents using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


... Cancel out the common terms.



So