数学高手来解答,带上过程!lga+lgb=2lg(a-2b),求：log(4)a/b=?

Question

数学高手来解答,带上过程!
lga+lgb=2lg(a-2b),求：log(4)a/b=?

Answer 1

lga+lgb=2lg(a-2b),
e^(lga+lgb)=e^2lg(a-2b),
e^lga*e^lgb=(e^lg(a-2b))^2
ab=(a-2b)^2
a^2-5ab+4b^2=0
(a-b)(a-4b)=0
a=b或a=4b
又a>0,b>0,a-2b>0
a=4b
a/b=4
log(4)a/b=1