Question

The value of ${\log _{10}}0.001$ is equal to
A. $ - 3$
B. 3
C. $ - 2$
D. 2

Answer 1

Hint: We will simplify the term 0.001 and write in powers of 10 as the base of the logarithm is 10 and then we can apply the property of logarithm. We will use the properties of logarithm such as ${\log _b}{a^n} = n{\log _b}a$ and ${\log _a}a = 1$ to get the required answer.

Complete step-by-step answer:
We have to find the value of ${\log _{10}}0.001$
We will first write 0.001 in powers of 10.
Then, $0.001 = {10^{ - 3}}$
Therefore, the above expression ${\log _{10}}0.001$ can be written as ${\log _{10}}{10^{ - 3}}$
Now, we know that ${\log _b}{a^n} = n{\log _b}a$
Hence, we can simplify the expression as
$ - 3{\log _{10}}10$
Also, we have the property of logarithm, ${\log _a}a = 1$
Then, the above expression is simplified as $ - 3\left( 1 \right) = - 3$
Therefore, the value of ${\log _{10}}0.001$ is $ - 3$
Hence, option A is correct.

Note: The concept of logarithm is used to simplify calculations. The inverse of logarithm function is an exponential function. The number ${\log _a}b = x$ is equivalent to ${a^x} = b$. Also, 0.001 is equivalent to $\dfrac{1}{{1000}}$ and ${10^{ - 3}}$.