Question

If $(3\cdot 7{)}^x=(0\cdot 037{)}^y=10000$ then value of $\frac{1}{x}-\frac{1}{y}$ is

• A. $\frac{3}{4}{\log }_{10}3.7$
• B. $2$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $\frac{3}{4}{\log }_{10}3.7$

We have, ${\left(3.7\right)}^x={\left(0.037\right)}^y=10000$

$x={\log }_{3.7}{10}^4$

$x=4{\log }_{3.7}10$

$\frac{1}{x}=\frac{1}{4}{\log }_{10}3.7$

$y={\log }_{0.037}{10}^4$

$y=4{\log }_{3.7}10$

$y=2{\log }_{3.7}10$

$\frac{1}{y}=\frac{1}{2}{\log }_{10}3.7$

$Now,$

$\frac{1}{x}-\frac{1}{y}=\frac{3}{4}{\log }_{10}3.7$

$Hence,theanswerAiscorrectanswer.$