Question

The value of ${\log }_{e}144$ is equal to

• A. $3{\log }_{e}2+{\log }_{e}18$
• B. $2{\log }_{e}12$
• C. $4{\log }_{e}2+2{\log }_{e}3$
• D. All of these

Answer 1

The correct option is D

All of these

$\Rightarrow {\log }_{e}144={\log }_e{12}^2=2{\log }_{e}12$
(Option A)

Factors of 144 = $2^4$ $\times$ $3^2$

$\therefore {\log }_{e}144={\log }_e(2^4\times 3^2)$

$={\log }_e{2}^4+{\log }_e{3}^2$

$=4{\log }_{e}2+2{\log }_{e}3$
(Option B)

$\Rightarrow {\log }_{e}144={\log }_e(2^3\times 18)$

$={\log }_e\left(2^3\right)+{\log }_{e}18$

$=3{\log }_{e}2$ + ${\log }_{e}18$
(Option C)

Hence the correct answer is Option D.