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

Question

If x = 1 + logabc , y = 1+ logbca , z = 1+
logcab , 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)

If x = 1 + logabc , y = 1+ logbca , z = 1+ logcab , prove that xyz = xy = yz + zx

If x = 1 + log_abc , y = 1+ log_bca , z = 1+ log_cab , prove that xyz = xy = yz + zx