How do you do this?

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.

Reply 1

C4>O7

Subst. in either (1) or (2):-
logap²q=9
=>logaq=9-2logap............(1)

logapq=5
=>logaq=5-logap...........(2)

Now:
logaq = logaq
=> 5-logap = 9-2logap
=> logap = 4

Subst. in (1):
logaq = 9-8
logaq = 1

Reply 2

El Stevo

DOJO

2 a , Express loga(QP^2) in terms of logaP and logaQ
2logaP+logaQ :tops:

DOJO

b) Given that loga(PQ)=5 and loga(QP^2) = 9, find the values of logaP and logaQ.
2logaP + logaQ = 9
logaP + logaQ = 5

logaP = 4

logaQ + logaP = 5
4 + logaQ = 5

logaQ = 1

Reply 3

he1c14h10

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

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?

Reply 4

Christophicus

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

Reply 5

DOJO

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.