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) (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) (Show Source): You can put this solution on YOUR website!
-\log_{8}\left(\sqrt{5}\right))
... Start with the given expression.
)
... Combine the logs using the identity .
)
... Factor 80 into 16*5.
)
... Break up the square root.
)
... Take the square root of 16 to get 4.
)
... Reduce
}{\log_{10}\left(8\right)})
... Use the change of base formula
Remember the change of base formula is
}{\log_{10}\left(2^3\right)})
... Rewrite each argument as a power of 2
}{3\log_{10}\left(2\right)})
... Pull down the exponents using the identity
... Cancel out the common terms.
So -\log_{8}\left(\sqrt{5}\right)=\frac{2}{3})
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