​ If x = loga bc, y = logb ca, z = logc ab, then prove that 1/1+x + 1/1+y + 1/1+z = 1. ​

Question

If x = log_a bc, y = log_b ca, z = log_c ab, then

prove that \(\frac1{1+x}+\frac1{1+y}+\frac1{1+z}=1\).

Answer 1

x = log_a (bc), y = log_b (ca), z = log_c (ab)

L.H.S. = \(\frac1{1+x}+\frac1{1+y}+\frac1{1+z}\)

= 1

= R.H.S.