Question

If x= log (a) bc, y= log (b) ca, z= log (c) ab
then prove x+y+z=xyz-2

Correct answer with full explanation then i will mark brainiest. please I'm struggling ​

Answer 1

Answer:

Hope it will help you

Step-by-step explanation:

a) x + y + z + 2 = xyz. x = logabc ⇒ ax = bc ⇒ ax + 1 = abc ⇒ a = (abc)1/(x +1) Similarly, b = (abc)1/(y + 1), c = (abc)1/(z + 1) ∴ abc = ( a b c ) 1 x + 1 + 1 y + 1 + 1 z + 1 (abc)1x+1+1y+1+1z+1 ⇒ 1 x + 1 + 1 y + 1 + 1 z + 1 1x+1+1y+1+1z+1 = 1 ⇒ (y + 1) (z + 1) + (x + 1) (z + 1) + (x + 1) (y + 1) = (x + 1) (y + 1) (z + 1) ⇒ yz + y + z + 1 + xz + x + z + 1 + xy + y + x + 1 = xyz + xy + yz + zx + x + y + z + 1 ⇒ x + y + z + 2 = xyz