Provide an appropriate response.
-Given that $\log _ { 10 } 5 = 0.699$, find $\log _ { 10 } \frac { 1 } { 625 }$ without using a calculator.
A) $- 20.000$
B) $0.342$
C) $- 2.796$
D) $- 8.388$

Question

Quizplus · Accepted Answer

First, recognize that $625 = 5^4$. Therefore, $\log_{10} \frac{1}{625} = \log_{10} 5^{-4}$. Using the property of logarithms that $\log_b a^n = n \log_b a$, we get $-4 \log_{10} 5$. Given $\log_{10} 5 = 0.699$, the calculation becomes $-4 \times 0.699 = -2.796$.

Provide an Appropriate Response log⁡105=0.699\log _ { 10 } 5 = 0.699log10​5=0.699

Provide an Appropriate Response $\log _ { 10 } 5 = 0.699$