Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 10 } ( 10,000 x )$
A) $4 + \log _ { 10 } \mathrm { x }$
B) $40 + \log _ { 10 } \mathrm { x }$
C) $4 \log _ { 10 } x$
D) $4 \mathrm { x }$

Question

Quizplus · Accepted Answer

The expression $\log _ { 10 } ( 10,000 x )$ can be expanded using the properties of logarithms. First, recognize that $10,000 = 10^4$, so the expression becomes $\log _ { 10 } ( 10^4 x )$. Using the property that $\log _ { a } ( b c ) = \log _ { a } b + \log _ { a } c$, this can be expanded to $4 + \log _ { 10 } x$, which matches choice A.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much