If $log 11 = 1.0414$ then prove that $10^{11} > 11^{10}$

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Solution

$10^{11} > 11^{10}$
Taking ${log}_{10}$ both side,
$11 {log}_{10} 10 > 10 {log}_{10} 11$
$11 > 10 (1.0414)$
$11 > 10.414$
Hence, proved $10^{11} > 11^{10}$

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