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