Rewrite the expression as a single logarithm and simplify the result. $\ln | \sec x | + \ln | \sin x |$
A) $\ln | \cos x |$
B) $\ln | \csc x |$
C) $\ln | \cot x |$
D) $\ln | \sin x |$
E) $\ln | \tan x |$

Question

Rewrite the expression as a single logarithm and simplify the result.​ $\ln | \sec x | + \ln | \sin x |$ ​
A) $\ln | \cos x |$
B) $\ln | \csc x |$
C) $\ln | \cot x |$
D) $\ln | \sin x |$
E) $\ln | \tan x |$

Quizplus · Accepted Answer

The properties of logarithms allow us to combine the two logarithms into one by multiplying their arguments: $\ln | \sec x | + \ln | \sin x | = \ln (| \sec x | \cdot | \sin x |)$. Since $\sec x = \frac{1}{\cos x}$, the expression simplifies to $\ln | \frac{1}{\cos x} \cdot \sin x | = \ln | \tan x |$, which matches choice E.

Rewrite the Expression as a Single Logarithm and Simplify the Result.​

Rewrite the Expression as a Single Logarithm and Simplify the Result.