Use properties of logarithms to evaluate the expression.
-$\log _ { 10 } ( 0.0001 ) ^ { 5 }$
A) $- 625$
B) $- 20$
C) $\frac { 1 } { 20 }$
D) $\log 625$

Question

Quizplus · Accepted Answer

The expression can be simplified using the power rule of logarithms, $\log_b(m^n) = n \log_b(m)$, giving $\log_{10}(0.0001^5) = 5 \log_{10}(0.0001)$. Since $\log_{10}(0.0001) = \log_{10}(10^{-4}) = -4$, the expression simplifies to $5 \times -4 = -20$.

Use Properties of Logarithms to Evaluate the Expression log⁡10(0.0001)5\log _ { 10 } ( 0.0001 ) ^ { 5 }log10​(0.0001)5

Use Properties of Logarithms to Evaluate the Expression $\log _ { 10 } ( 0.0001 ) ^ { 5 }$