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.