Question

Which one of the two is greater ?

${\log }_{2}3or{\log }_{1/2}5$

• A. ${\log }_{2}3$
• B. ${\log }_{1/2}5$
• C. Both are equal
• D. Can't say

Answer 1

The correct option is A ${\log }_{2}3$

Let ${\log }_{2}3=x$

$\therefore 2^x=3$

$\therefore x>1$

Let ${\log }_{1/2}5=y$

$\therefore {\left(\frac{1}{2}\right)}^y=5$
or $2^y=\frac{1}{5}$

$\therefore y<1$

or $1>y$

$x>y$

$\Rightarrow {\log }_{2}3>{\log }_{1/2}5$