Answer:
14. 5log3(x) -2log3(y)
18. ln(x+1) -2ln(x)
Step-by-step explanation:
The relevant rules of logarithms are ...
log(ab) = log(a) +log(b)
log(a^b) = b·log(a)
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14. Applying the first rule gives ...
log3(x^5) +log3(y^-2)
Applying the second rule gives ...
5·log3(x) -2·log3(y)
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18. The log of a sum cannot be simplified. We can make this be a simpler expression so that the log of it will be fairly simple.
ln(1/x +1/x^2) = ln(x/x^2 +1/x^2) = ln((x+1)/x^2)
Now, we can apply rule 1 to get ...
ln(x+1) +ln(1/x^2)
and applying rule 2 gives ...
ln(x+1) -2ln(x)
