2loga (m-n) = logam + Logan, then the value of N / M is? How to calculate

2loga (m-n) = logam + Logan, then the value of N / M is? How to calculate

loga(m-n)²=logamn
(m-n)²=mn
m²-3mn+n²=0
(n/m)²-3(n/m)+1=0
n/m=(3±√5)/2
Because M-N > 0
So n / M = (3 - √ 5) / 2

If 2loga (m-2n) = logam + Logan, the value of Mn is______ ．

Because 2loga (m-2n) = logam + Logan, so loga (m-2n) 2 = loga (MN), so (m-2n) 2 = Mn, so m2-4mn + 4n2 = Mn, so (MN) 2 − 5MN + 4 = 0, so Mn = 4 or 1, because m > 2n, so Mn = 4, so the answer is: 4

logaM+logaN=_______ (a > 0 and a is not equal to 1, M > 0, n > 0)
According to the operation rule of power: A ^ n + A ^ m = a ^ (M + n) and the meaning of the book, the above conclusion is proved

Let logam = x, Logan = y
∴a^x=M,a^y=N
∴M*N=a^x+a^y=a^(x+y)
∴logaM+logaN=x+y=logaa^(x+y)=logaM*N