Question

The exponential form of ${\log }_{10}0.001=-3$ is ____
A.$(0.001{)}^{10}=-3$
B.$(-3{)}^{10}=0.001$
C.$(10{)}^3=-0.001$
D.$(10{)}^{-3}=0.001$

Answer 1

Hint: Use the information, ${\log }_{b}a=c\Rightarrow a=b^c$.

We know that, ${\log }_{b}a=c\Rightarrow a=b^c$ So ${\log }_{10}0.001=-3\Rightarrow 0.001={10}^{-3}$. Hence Option D is correct.
Note: Base of the log and the value inside the log, cannot be negative. Otherwise log will give imaginary values.