Question

${\log }_{25}36=$ ?

• A. $2{\log }_{25}6$
• B. $\frac{1}{2}$ ${\log }_{5}36$
• C. ${\log }_{5}6$
• D. All of these

Answer 1

The correct option is D

All of these

Let y = ${\log }_{25}36$

= $\frac{{\log }_{e}36}{{\log }_{e}25}=\frac{{\log }_e{6}^2}{{\log }_e{5}^2}=\frac{2{\log }_{e}6}{2{\log }_{e}5}=\frac{{\log }_{e}6}{{\log }_{e}5}$

= ${\log }_{5}6$

${\log }_{25}36$ can be written as,

${\log }_{5^2}{6}^2=2{\log }_{5^2}6$
or $\frac{1}{2}{\log }_5{6}^2$