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Logarithms

Express log...

Question

Express ${log}_{10} \sqrt[5]{108}$ in terms of ${log}_{10} 2$ and ${log}_{10} 3$ .

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Solution

${log}_{10} \sqrt[5]{108} = {log}_{10} \sqrt[5]{2^{2} \times 3^{3}}$

$= {log}_{10} (2)^{\frac{2}{5}} (3)^{\frac{3}{5}}$

$= \frac{2}{5} {log}_{10} 2 + \frac{3}{5} {log}_{10} 3$

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