If $2 {log}_{10} x + 1 = {log}_{10} 250$ , then the value of ${log}_{10} 2 x$ is equal to

9

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5

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11

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1

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Solution

The correct option is D $1$
$x > 0$
$2 {log}_{10} x + 1 = {log}_{10} 250 {log}_{10} x^{2} + {log}_{10} 10 = {log}_{10} 250 {log}_{10} 10 x^{2} = {log}_{10} 250 Removing log 10 x^{2} = 250 x^{2} = 25 x = 5$
$∴ {log}_{10} 2 x = {log}_{10} (2 \times 5) = {log}_{10} 10 = 1$

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