Question

Based on this information answer the question given

If $(a>1,x>1)$ or $(0<a<1,0<x<1)$.

then ${\log }_{a}x>0$ i.e., ${\log }_{a}x$ is positive.

If $(0<a<1,x>1)$ or $(a>1,0<x<1)$, then ${\log }_{a}x<0$

If $a>b$ then ${\log }_{b}a>1$ and ${\log }_{a}b<1$

Which is greater ${\log }_{2}11$ or ${\log }_{11}2$

• A. ${\log }_{2}1$
• B. ${\log }_{2}11$
• C. ${\log }_{2}81$
• D. None of the above

Answer 1

Answer: (B)

${\log }_{2}11$

Given ${\log }_{2}11,{\log }_{11}2$

According to the passage

If $a>b$ then ${\log }_{b}a>1$ and ${\log }_{a}b<1$

here $a=11,b=2$

$\Rightarrow {\log }_{2}11>1$ where as ${\log }_{11}2<1$

$\Rightarrow {\log }_{2}11>{\log }_{11}2$

$\therefore$ the greater of the two is ${\log }_{2}11$