Question

一道有关对数运算的高一数学题lga+lgb=2lg(a-2b),求a/b的值

Answer 1

lga+lgb=2lg(a-2b),求a/b的值

Lg(ab)=Lg(a-2b)^2

ab=(a-2b)^2

ab=a^2-4ab+4b^2

5ab=a^2+4b^2,两边同除以b^2得

5(a/b)=(a/b)^2+4

(a/b)^2-5(a/b)+4=0

[(a/b)-1][(a/b)-4]=0

∴a/b=1或a/b=4