Simple question about logarithm quotient rule
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Simple question about logarithm quotient rule

[From: ] [author: ] [Date: 11-05-19] [Hit: ]
So,Expand the negative into the brackets.......
If I take the ln of y= (ab)/(cd) is that going to be lna+lnb-lnc+lnd or lna+lnb-lnc-lnd?

...to put it simply, I'm asking if I should subtract the whole quantity of the divisor or just the first one?

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Try splitting it into two steps. First, consider that

ln y = (ab)/(cd) = ln (ab) - ln (cd)

Then you know that
ln (ab) = ln (a) + ln (b)
and that
ln (cd) = ln (c) + ln (d)

So, now make the substitution in
ln (ab) - ln (cd) = [ln (a) + ln (b)] - [ln (c) + ln (d)]

Expand the negative into the brackets.

ln y = ln (a) + ln (b) - ln (c) - ln (d)
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