Question

if a=Log base x(yz) , b=log base y(zx) and c=log base z(xy) then prove that 1/(a+1)+1/(b+1)+1/(c+1)=1

Answer 1

1/(a+1)+1/(b+1)+1/(c+1)
=1/(log base x(yz) +1) + 1/( log base y(zx) +1 ) +1/(log base z(xy) +1)
=(log x/ log y+ log z + log x) + (log y/ log z + log x +log y ) + (log z / log x +log y + log z)
=logx +log y + log z / log x +log y +log z
=1
hence proved

Answer 2

1/(a+1)+1/(b+1)+1/(c+1)
=1/(log base x(yz) +1) + 1/( log base y(zx) +1 ) +1/(log base z(xy) +1)
=(log x/ log y+ log z + log x) + (log y/ log z + log x +log y ) + (log z / log x +log y + log z)
=logx +log y + log z / log x +log y +log z
=1