Question

If $A={\log }_{13}189;B={\log }_{23}521$, which of the following is correct?

• A. $A<B$
• B. $A=B$
• C. $A>B$
• D. $A\le B$

Answer 1

The correct option is C $A>B$

$A={\log }_{13}189$

$\Rightarrow {13}^A=189$

As we know that, ${13}^2=169$

Hence, $A>2$

Similarly,

$B={\log }_{23}521$

$\Rightarrow {23}^B=521$

As we know that, ${23}^2=529$

Hence, $B<2$

So, $A>B$