Question

If $lo{g}_{10}x-lo{g}_{10}\sqrt{x}=\frac{2}{lo{g}_{10}x}$, then value of x is

• A. $\frac{1}{100}$ or $100$
• B. $\pm$ 2
• C. 10 or $\frac{1}{10}$
• D. 100

Answer 1

Answer: (A)

$\frac{1}{100}$ or $100$

Given, $lo{g}_{10}x-lo{g}_{10}\sqrt{x}=\frac{2}{lo{g}_{10}x}$

$lo{g}_{10}\frac{x}{\sqrt{x}}=\frac{2}{lo{g}_{10}x}$

$lo{g}_{10}\sqrt{x}=\frac{2}{lo{g}_{10}x}$

$\frac{1}{2}lo{g}_{10}x=\frac{2}{lo{g}_{10}x}$

$\frac{1}{2}(lo{g}_{10}x{)}^2=2$

$(lo{g}_{10}x{)}^2=4$

$lo{g}_{10}x=\pm 2$

$x={10}^{\pm 2}$

$x=100or\frac{1}{100}$

Hence, this is the answer.