**Determine the value of (P+Q) given that: Plog _{400}5 + Qlog_{400}2 = 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:*

Plog_{400}5 + Qlog_{400}2 = 3

log_{400}(5^{p} x 2^{q}) = 3

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

MapleTheory
Dec 28, 2017

#1**+3 **

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

#2**+1 **

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

#3**+2 **

No, its fine. I got up to 400^{3}= 5^{p} x 2^{q} , but never thought of converting 400 to (2^{4} x 5^{2}). Wow! Thanks very much Melody!

MapleTheory
Dec 28, 2017