Question

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

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

Answer 1

The correct option is C $A>B$

$A={\log }_{13}189={\log }_{13}({13}^2+20)$

and $B={\log }_{23}521={\log }_{23}({23}^2-8)$

$\therefore A>B$ ($A>2$ and $B<2$)