Evaluate the expression. $\log \sqrt { 0.0001 }$
A) $- 1$
B) $2$
C) $- 2$
D) $- \frac { 1 } { 2 }$
E) $\frac { 1 } { 3 }$

Question

Quizplus · Accepted Answer

We can rewrite $\sqrt{0.0001}$ as $0.0001^{\frac{1}{2}}$. Then, using the property $\log_a b^c=c\log_a b$, we have:

$$\log \sqrt { 0.0001 }=\log {0.0001^{\frac{1}{2}}}=\frac{1}{2}\log {0.0001}$$

Next, we can use the fact that $\log_{10}0.0001=-4$ (since $10^{-4}=0.0001$).

Therefore, $\frac{1}{2}\log {0.0001}=\frac{1}{2}(-4)=-2$, giving us the final answer of $-2$. Thus, the best choice is C.

Evaluate the Expression log⁡0.0001\log \sqrt { 0.0001 }log0.0001​ A) −1- 1−1 B) 222