Question

prove that log 7 base 6 = log 7 base 2 ÷ 1 + Log 3 base 2

Answer 1

Answer:

log₆7 = log₂7 / (1 + log₂3)

Step-by-step explanation:

to prove log₆7 = log₂7 / (1 + log₂3)

take RHS = log₂7 / (1 + log₂3)

               = log₂7 / (log₂2 + log₂3)           [ ∵  logₐa = 1 ]

               = log₂7 / log₂(2*3)                     [ ∵  logₐx + logₐy = logₐ xy ]

               = log₂7 / log₂6

               = log₆7                                       [ ∵  logₙ x / logₙ a  = logₐ x ]

               = LHS

=> RHS = LHS

Hence proved