SOLUTION: If log (p+q) = log p- log q, show that p(1-q)=q^2

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Question 87655: If log (p+q) = log p- log q, show that p(1-q)=q^2
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Remember the law of logarithms: log+%28p%2Fq%29+=+log+p+-+log+q+.

Therefore, if you are given that log+%28%28p%2Bq%29%29+=+log+p-+log+q,
then replace the right side as follows:log+%28%28p%2Bq%29%29+=+log%28p%2Fq%29+

Take the antilog of each side and it looks like this: %28p%2Bq%29+=+%28p%2Fq%29
Muliply both sides by q: q%28p%2Bq%29+=+p
pq%2B+q%5E2+=+p+

Subtract pq from each side:
q%5E2+=+p-pq+

Factor the right side:
q%5E2+=+p%281-q%29+
p%281-q%29=q%5E2

R^2 Retired from SCC