Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 4 } ( 16 x )$

A) $2 x$
B) $8 + \log _ { 4 } x$
C) $2 \log _ { 4 } x$
D) $2 + \log _ { 4 } x$

Question

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 4 } ( 16 x )$

A) $2 x$
B) $8 + \log _ { 4 } x$
C) $2 \log _ { 4 } x$
D) $2 + \log _ { 4 } x$

Quizplus · Accepted Answer

The expression can be expanded using the properties of logarithms. Specifically, $\log _ { 4 } ( 16 x )$ can be rewritten as $\log _ { 4 } ( 4^2 x )$, which simplifies to $2 + \log _ { 4 } x$ using the properties $\log_b (a \cdot c) = \log_b a + \log_b c$ and $\log_b (b^a) = a$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much