Question

x=logbc/loga,y=logca/logb,z=logab/logc .prove it —x+y+z=xyz–2

Answer 1

x=logabc⇒ax=bxy=logbca⇒by=caz=logcabcz=aba(xyz)=(ax)yz=(bc)yz=(byz)(cyz)=(by)z(cz)y=(ca)z(ab)y=cz.az.ay.by=ab.ay+z.(ca)=bc.ay+z.a2=ax.ay+z.a2⇒a(xyz)=ax+y+z+2⇒xyz=x+y+z+2⇒xyz−x−y−z=2 (Answer)

Hope this information will clear your doubts about this topic.

Answer 2

x = log a (bc)  

y= log b (ca)

z= log c (ab)

Prove that :

x+ y + z + 2 = xyz

We will start from left side:

x+ y + z + 2 = log a (bc) + log b (ca) + log c (ab) + 2

We know that: log b (x) = log a (x) + log a (b)

Let us the base 10 as a:

==>  (log bc/ log a)+(log ca/log...