The value of $(2^{(l o g_{6} 18)}) . (3^{(l o g_{6} 3)})$ is

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Solution

The correct option is A 6
$2^{l o g_{6}^{18}} \cdot 3^{l o g_{6}^{3}}$
$18^{l o g_{6}^{2}} \cdot 3^{l o g_{6}^{3}} = (6 \times 3)^{l o g_{6}^{2}} \cdot 3^{l o g_{6}^{3}}$
$= 6^{l o g_{6}^{2}} \cdot 3^{l o g_{6}^{2}} \cdot 3^{l o g_{6}^{3}}$
$= (2) 3^{l o g_{6}^{2} + l o g_{6}^{3}}$
$= (2) 3^{l o g_{6}^{2 (3)}}$
$= (2) 3^{l o g_{6}^{6}}$
$= (2) (3) = 6$ .

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