Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as
possible.
-$$\frac { 1 } { 2 } \log _ { 2 } p + 4 \log _ { 2 } 3$$
A) $\log _ { 2 } ( \sqrt { p } + 81 )$
B) $\log _ { 2 } \frac { p + 24 } { 2 }$
C) $\log _ { 2 } ( 81 \sqrt { p } )$
D) $\log _ { 2 } 6 p$

Question

Quizplus · Accepted Answer

The expression can be simplified using logarithm properties: $\frac { 1 } { 2 } \log _ { 2 } p$ becomes $\log _ { 2 } \sqrt { p }$, and $4 \log _ { 2 } 3$ becomes $\log _ { 2 } 3^4$ or $\log _ { 2 } 81$. Combining these using the product rule for logarithms gives $\log _ { 2 } ( 81 \sqrt { p } )$.

Write the Logarithmic Expression as a Single Logarithm with Coefficient 12log⁡2p+4log⁡23\frac { 1 } { 2 } \log _ { 2 } p + 4 \log _ { 2 } 321​log2​p+4log2​3

Write the Logarithmic Expression as a Single Logarithm with Coefficient $\frac { 1 } { 2 } \log _ { 2 } p + 4 \log _ { 2 } 3$