If ` log_(a)b=2, log_(b)c=2, and log_(3) c= 3 + log_(3)` a,then the value of c/(ab)is ________.

Answer

3

Explanation

` log_(3) c = 3 + log _(3) a `
` or log_(3) c/a = 3 or c = 27 a ` …(i)
` log_(a) b = 2, log_(b) c = 2`
` rArr log_(a) b* log _(b) c = 4`
` rArr log_(a) c = 4`
` rArr c = 4^(4)`...(ii)
From Eqs.(i) and (ii), we get a = 3, c = 81.
From ` log_(a) b = 2," we have " b = a^(2) = 9`.
Hence, c/(ab) = 3.