Evaluate
${log}_{3}^{5} . {log}_{5}^{9} . {log}_{9}^{3}$ ?

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Solution

${log}_{3} 5 {log}_{5} 9 {log}_{9} 3$
$= \frac{log 5}{log 3} \times \frac{log 9}{log 5} \times \frac{log 3}{log 9}$
$= 1$

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