SOLUTION: Write the expression as a single natural logarithm. ln a-2 ln b+1/2 ln c Thanks for your help.

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Question 30180: Write the expression as a single natural logarithm.
ln a-2 ln b+1/2 ln c
Thanks for your help.

Answer by sdmmadam@yahoo.com(530) About Me  (Show Source):
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Write the expression as a single natural logarithm.
ln a-2 ln b+1/2 ln c
Thanks for your help
(ln a)- 2(ln b)+1/2 (ln c)
=log(a)-log(b^2)+log[c^(1/2)] ( using n[log m)]= log(m^n))
=log(a)+log[c^(1/2)]-log(b^2)
(by additive commutativity (second and third terms)
= {log(a)+log[c^(1/2)]}-log(b^2) (by additive associativity)
=log{a[c^(1/2)]}-log(b^2) (using sum of logarithms = log of product)
=log{a[c^(1/2)]/(b^2)} to the base e of course as we are talking about natural logarithms.
Answer:log[a(c^(1/2))/b^2]