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2 a , Express loga(p^2q) in terms of logap and logaq

That is:

2logaP+logaQ

b) Given that loga(pq)=5 and loga(p^2q) = 9, find the values of logaq and logaq.

I turned it into a simulataneous equation and got a value logaP = 4, but I am unsure on what to do next.

All help appreciated.

That is:

2logaP+logaQ

b) Given that loga(pq)=5 and loga(p^2q) = 9, find the values of logaq and logaq.

I turned it into a simulataneous equation and got a value logaP = 4, but I am unsure on what to do next.

All help appreciated.

Given that loga(pq)=5 and loga(p²q) = 9, find the values of logaq and logaq.

logapq = logaq + logaq = 5

logaq = 5 - logaq (1)

loga(p²q) = 9

logap² + logaq = 9

2logap + logaq = 9 (2)

(1) into (2)

2(5 - logaq) + logaq = 9

10 - 2logaq + logaq = 9

logaq = 1

From (1)

logaq = 5 - logaq

logaq = 5 - 1 = 4

logapq = logaq + logaq = 5

logaq = 5 - logaq (1)

loga(p²q) = 9

logap² + logaq = 9

2logap + logaq = 9 (2)

(1) into (2)

2(5 - logaq) + logaq = 9

10 - 2logaq + logaq = 9

logaq = 1

From (1)

logaq = 5 - logaq

logaq = 5 - 1 = 4

he1c14h10

if you got logap=4 , you will certainly get logaq=1, and those are all what they are asking in the question. So what are you looking for?

ahh I thought so.

Yeah, I was going to insert that into equation 1. But I just wanted to double check my method on here, as this is a past exam question.

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can someone please explain what principle domain is and why the answer is a not c?Maths

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