If the value of ${log}_{25} 125 - {log}_{8} 4$ is k.Find 6k

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Solution

Given ${log}_{25} 125 - {log}_{8} 4$
${log}_{5^{2}} 5^{3} - {log}_{2^{3}} 2^{2} = \frac{3}{2} {log}_{5} 5 - \frac{2}{3} {log}_{2} 2$
$= \frac{3}{2} - \frac{2}{3}$ $[∵ {log}_{a} = 1]$
$= \frac{5}{6}$

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