Given: $2 {log}_{10^{x}} + 1 = {log}_{10} 250$ . Find $x$ and ${log}_{10} 2 x$

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Solution

$2 {log}_{10} x + {log}_{10} 10 = {log}_{10} 250$
$= {log}_{10} x^{2} + {log}_{10} 10 = {log}_{10} 250$
$∴ 10 x^{2} = 250 \Rightarrow x = 5$
${log}_{10} 2 x = {log}_{10} 10 = 1$

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