Question

State whether statement is true or false ${\log }_{2}17{\log }_{1/5}2lo{g}_3\frac{1}{5}>2.$

• A. True
• B. False

Answer 1

The correct option is A True

We have,

${\log }_{2}17{\log }_{1/5}2{\log }_3\frac{1}{5}>2$

We know that

${\log }_{n}m=\frac{\log m}{\log n}$

Therefore,

${\log }_{2}17.\frac{\log 2}{\log 1/5}.\frac{\log 1/5}{\log 3}>2$

${\log }_{2}17.\frac{\log 2}{\log 3}>2$

${\log }_{2}17.\frac{1}{\frac{\log 3}{\log 2}}>2$

${\log }_{2}17.\frac{1}{{\log }_{2}3}>2$

${\log }_{3}17>2$

Since, ${\log }_{3}17>2.6$

Hence, this is the answer.