Question

若2loga(M-2N)=logaM+logaN,求M/N值

Answer 1

∵2loga(M-2N)=logaM+logaN,

且 2loga(M-2N)=loga(M-2N)^2

logaM+logaN=logaMN

∴(M-2N)^2=MN

∴M^2-5MN+4N^2=0

即(M-N)(M-4N)=0

M/N=1或M/N=4

又∵M-2N＞0,

∴M/N=1舍去

综上：M/N=4