Question

If $\frac{1}{{\log }_{x}10}=\frac{3}{lo{g}_{p}10}-3$, then $x=$

• A. $100p^2$
• B. $\frac{p^2}{100}$
• C. $1000p^3$
• D. $\frac{p^3}{1000}$

Answer 1

Answer: (D)

$\frac{p^3}{1000}$

Given,

$\frac{1}{{\log }_{x}10}=\frac{3}{{\log }_{p}10}-3$

${\log }_{10}x=3{\log }_{10}p-3$ $({\log }_{b}a=\frac{1}{{\log }_{a}b})$

${\log }_{10}x=3({\log }_{10}p-1)$

$=3({\log }_{10}p-{\log }_{10}10)$

${\log }_{10}x={\log }_{10}(\frac{p}{10}{)}^3$

$x=(\frac{p}{10}{)}^3=\frac{p^3}{1000}$