Determine the value of (P+Q) given that: Plog4005 + Qlog4002 = 3


Hi, I've been having trouble lately with this question. I've tried completing it, but so far I have only got up to this:


Plog4005 + Qlog4002 = 3


log400(5p x 2q) = 3


I'm stuck on what to do next, your help will much be appreciated! Thanks! 

MapleTheory  Dec 28, 2017
edited by MapleTheory  Dec 28, 2017

3+0 Answers


Hi MapleTheopry,

This is an unusual question. :)


\(Plog_{400}5+Qlog_{400}2=3\\ log_{400}(5^P)+log_{400}(2^Q)=3\\ log_{400}(5^P*2^Q)=3\\~\\ 400^3=5^P*2^Q\\ (2^4*5^2)^3=5^P*2^Q\\ 2^{12}*5^6=2^Q*5^P\\ so\\ P+Q=6+12=18 \)

Melody  Dec 28, 2017

For some reason LaTex is not displaying properly.

If you cannot make sense of my answer let me know and I will try to write it without LaTex. :/

Melody  Dec 28, 2017

No, its fine. I got up to 4003= 5p x 2q , but never thought of converting 400 to (24 x 52). Wow! Thanks very much Melody! 

MapleTheory  Dec 28, 2017

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