Question

Which of the following is "NOT" equivalent to ${\log }_{3}27?$

• A. $\frac{{\log }_{2}27}{{\log }_{2}3}$
• B. $3$
• C. $\frac{1}{{\log }_{27}3}$
• D. $\frac{{\log }_{2}27}{{\log }_{27}3}$

Answer 1

The correct option is D $\frac{{\log }_{2}27}{{\log }_{27}3}$

Given: ${\log }_{3}27={\log }_3{3}^3=3$
Using ${\log }_a{x}^m=m{\log }_{a}x$
${\log }_{3}27=\frac{1}{{\log }_{27}3}$
$\because {\log }_{b}a=\frac{1}{{\log }_{a}b}$
${\log }_{3}27=\frac{{\log }_{2}27}{{\log }_{2}3}$
$\because {\log }_{b}a=\frac{{\log }_{m}a}{{\log }_{m}b}$