Use the properties of logarithms to evaluate $\log _ { 10 } \left( \frac { 1 } { 100 } \right) ^ { 3 }$ without a calculator.
A) -6
B) -8
C) $\frac { 1 } { 8 }$
D) 6
E) $\frac { 3 } { 2 }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, $\log _ { 10 } \left( \frac { 1 } { 100 } \right) ^ { 3 }$ can be simplified as $3 \log _ { 10 } \left( \frac { 1 } { 100 } \right)$. Since $\log _ { 10 } 100 = 2$, and $\log _ { 10 } \left( \frac { 1 } { 100 } \right) = -2$, the expression simplifies to $3 \times -2 = -6$.

Use the Properties of Logarithms to Evaluate log⁡10(1100)3\log _ { 10 } \left( \frac { 1 } { 100 } \right) ^ { 3 }log10​(1001​)3

Use the Properties of Logarithms to Evaluate $\log _ { 10 } \left( \frac { 1 } { 100 } \right) ^ { 3 }$