Question

Evaluate the following logarithmic expression without calculator:
${\log }_{2}16$ and ${\log }_3^{}27$

• A. ${\log }_{2}16=8$ and ${\log }_{3}27=3$
• B. ${\log }_{2}16=4$ and ${\log }_{3}27=3$
• C. ${\log }_{2}16=4$ and ${\log }_{3}27=9$
• D. None of the above

Answer 1

The correct option is B ${\log }_{2}16=4$ and ${\log }_{3}27=3$

We know that, ${\log }_{x}x=1$

${\log }_{2}16={\log }_2{2}^4=4{\log }_{2}2=4$
${\log }_{3}27={\log }_3{3}^3=3{\log }_{3}3=3$