Question

If a^2+b^2=7ab,then log(a-b÷
$\sqrt{5}$

Answer 1

a²+b²=7ab,

then

a²+b²-2ab=7ab-2ab,

(a-b)²=5ab,

then

(a-b)=√(5ab),


therefore

log[(a-b÷√5],

log[√(5ab) ÷ √5],

log√(ab),

log[ab]^(1/2),

1/2 log(ab),

1/2 [loga+logb]