What is the value of $l o g_{9} 27 + l o g_{8} 32 ?$

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\frac{19}{6}

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\frac{7}{2}

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Solution

The correct option is C $\frac{19}{6}$

$l o g_{9} 27 + l o g_{8} 32$

= $\frac{l o g 27}{l o g 9} + \frac{l o g 32}{l o g 8}$

= $\frac{l o g 3^{2}}{l o g 3^{2}} + \frac{l o g 2^{5}}{l o g 2^{3}}$

= $\frac{3 l o g 3}{2 l o g 3} + \frac{5 l o g 2}{3 l o g 2}$

= $\frac{3}{2} + \frac{5}{3}$
= $\frac{19}{6}$

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