Question 1030330: Condense the expression to a logarithm of a single quantity. logx-2logy+3logz
Answer by mathmate(429)   (Show Source):
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Question:
Condense the expression to a logarithm of a single quantity. logx-2logy+3logz
Solution:
Use the laws of logarithms,
1. log(ab)=log(a)+log(b)
2. log(a/b)=log(a)-log(b)
3. log(a^b)=b*log(a)
These laws apply to logarithms of any base, but the bases on each side of the equal sign must be the same.
We're given
log(x)-2log(y)+3log(z)
=log(x)-log(y²)+log(z³) [ using law #3]
=log(xz³/y²) [using laws #1 and #2, and commutativity of both multiplication and addition]
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