Evaluate ${log}_{3} 2 {log}_{4} 3 {log}_{5} 4..... {log}_{15} 14 {log}_{16} 15$

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Solution

${log}_{3} 2 {log}_{4} 3 {log}_{5} 4..... {log}_{15} 14 {log}_{16} 15$
$= {log}_{16} 2 = {log}_{2^{4}} 2 = \frac{1}{4} {log}_{2} 2 = \frac{1}{4}$

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