plz ans fast from chap logarithmn
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Clearly, we know that
log a base b = 1/ log b base a
Using this property of logarithm we say that
LHS = 1/log 42 base 2 + 1/log 42 base 3 + 1/ log 42 base 7
= log 2 base 42 + log 3 base 42 + log 7 base 42
Now, using addition property of logarithm that the arguments of individual logarithm multiply to give the logarithm to the same base.
that is
log A + log B = log AB to the same base (also provided that the bases of the logarithm are both same)
So,
log 2 base 42 + log 3 base 42 + log 7 base 42 = log ((2)(3)(7)) base 42 = log 42 base 42 = 1 = RHS
Since ,log A base A = 1
Hence, proved.
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