Answer :

log100.16 = 2log104 - 2


Let us consider the RHS:


i.e. 2log104 - 2 = 2log104 - 2log1010


= log1042 - log10102


( logaMn = nlogaM)


=


( loga(M ÷ N) = (logaM) - (logaN))


= log10(0.16) = log100.16


Hence LHS = RHS


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