Question

Find the value of ${\log }_e$ 144.

• A. 2 log_e 12
• B. 4 log_e 2+2 log_e 3
• C. log_e 2 + log_e 18
• D. All of these

Answer 1

The correct option is D

All of these

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

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

${\log }_e$ 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)

${\log }_e$ 144 = ${\log }_e$ ($2^3$ $\times$ 18) = ${\log }_e\left(2^3\right)$ + $\log 18$

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