Express $2 {log}_{e} 2 + 3 {log}_{e} n$ as the logarithm of a single quantity.

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Solution

Applying the logarithm laws,

$2 {log}_{e} 2 + 3 {log}_{e} n$

$= {log}_{e} 4 + {log}_{e} n^{3}$

$= {log}_{e} 4 n^{3}$

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