Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log \left( \frac { x } { 100 } \right)$
A) $\log x - 2$
B) $\log x + 2$
C) $- 20 x$
D) $100 x$

Question

Quizplus · Accepted Answer

The expression can be expanded using the quotient rule of logarithms, $\log_b \frac{M}{N} = \log_b M - \log_b N$, and the fact that $\log_b b^k = k$, to get $\log x - \log 100$. Since $\log 100 = 2$ (because $100 = 10^2$ and the base of the logarithm is 10 by default), the expression simplifies to $\log x - 2$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much