Find the value of ${log}_{9} 9 + {log}_{9} 81 + {log}_{9} 729$

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Solution

Let $a = {log}_{9} 9 + {log}_{9} 81 + {log}_{9} 729$

$= {log}_{9} 9 + {log}_{9} 9^{2} + {log}_{9} 9^{3}$

$= {log}_{9} 9 + 2 {log}_{9} 9 + 3 {log}_{9} 9$

$= 1 + 2 + 3 = 6$

$∴ {log}_{9} 9 + {log}_{9} 81 + {log}_{9} 729 = 6$

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