Q11 If x = 1 + logabc, y = 1 + logbca, z = 1 + logcab prove that - Maths - Sets

Question

Q11 If x = 1 + log a b c ,   y   =   1   +
  log b c a ,   z   =   1   +   log c
a b prove that xyz = xy + yz + zx

Vipin Verma · Accepted Answer

x =1+logabc , y = 1+logbca , z = 1+logcabFrom the property of logarithm , we have logpq =logsplogsq , logss = 1As xy + yz + zx = xzyOr 1x+1y+1z =1And x =1+ logabc , y = 1+logacalogab , z = 1+logaablogacSo 1x+1y+1z= 11+ logabc + logab logab + logaca + logac logac + logaab= logaa logaa+ logabc + logab logab + logaca + logac logac + logaab= logaa + logab+ logac logaabc= logaabc logaabc = 1 (hence proved)

Q11. If x = 1 + log a b c , y = 1 + log b c a , z = 1 + log c a b prove that xyz = xy + yz + zx

Q11. If x = 1 + $\log_{a} b c, y = 1 + \log_{b} c a, z = 1 + \log_{c} a b$ prove that xyz = xy + yz + zx