# 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

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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.

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.

Last updated date: 26th Sep 2023

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