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Explanation:

13log3M+3log3N+1+log0.0085...(i)

Consider the R.H.S of (i):

1+log0.0085=1+log5log0.008=1+log(102)log(81000)=1+log10log2log8log1000=1+log10log23log23log10

=1+log10log23(log10log2)=113=23 ...(ii)

Consider the L.H.S of (i):

13log3M+3log3N

=log3M1/3+log3N3=log3(M1/3N3) ....(iii)

Equating equations (ii) and (iii), we get,

log3(M1/3N3)=23M1/3N3=32/3

Cubing both sides, we get,

M × N9 = 9

N9=9M

Hence, option (b).

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