Which of the following is the largest number?
A) 2 ln 2 + ln 3
B) ln 6 - ln 1
C) $\frac { 3 } { 2 }$ ln 16 - ln 8
D) $\frac { 1 } { 2 }$ ln 16
E) $\frac { 1 } { 3 }$ ln 27

Question

Quizplus · Accepted Answer

Using properties of logarithms, we can simplify each option to compare them directly. A) $2 \ln 2 + \ln 3 = \ln(4) + \ln(3) = \ln(12)$B) $\ln 6 - \ln 1 = \ln(6/1) = \ln(6)$C) $\frac { 3 } { 2 } \ln 16 - \ln 8 = \ln(16^{3/2}) - \ln(8) = \ln(64) - \ln(8) = \ln(8)$D) $\frac { 1 } { 2 } \ln 16 = \ln(16^{1/2}) = \ln(4)$E) $\frac { 1 } { 3 } \ln 27 = \ln(27^{1/3}) = \ln(3)$Comparing the simplified forms, $\ln(12)$ is the largest value.

Which of the Following Is the Largest Number? A) 2 32\frac { 3 } { 2 }23​

Which of the Following Is the Largest Number?
A) 2 $\frac { 3 } { 2 }$