Express as a single logarithm and, if possible, simplify.
-$\ln ( 32 x + 16 ) - 2 \ln 4$
A) $\ln ( 32 x )$
B) $\ln ( 4 x + 2 )$
C) $\ln ( 2 x + 1 )$
D) $\ln ( 256 ( 2 x + 1 ) )$

Question

Quizplus · Accepted Answer

The expression simplifies to $\ln ( 32 x + 16 ) - \ln 16$ using the property $b \ln a = \ln a^b$, which further simplifies to $\ln \frac{32x + 16}{16}$ using the property $\ln a - \ln b = \ln \frac{a}{b}$. Simplifying the fraction inside the logarithm gives $\ln (2x + 1)$.

Express as a Single Logarithm And, If Possible, Simplify ln⁡(32x+16)−2ln⁡4\ln ( 32 x + 16 ) - 2 \ln 4ln(32x+16)−2ln4

Express as a Single Logarithm And, If Possible, Simplify $\ln ( 32 x + 16 ) - 2 \ln 4$