log0.001 =-3

To understand why log0.001 is equal to -3, we need to first understand logarithms and their properties.

Logarithms are used to solve equations where a variable is an exponent. They represent the inverse operation of exponentiation. In simple terms, if we have an equation like x = b^a, the logarithm of x with base b is represented as log(base b) x = a.

In this case, we have log0.001, which means we need to find the exponent to which we raise the base 10 to get 0.001.

So, log0.001 (base 10) = x can be rewritten as 10^x = 0.001.

To solve for x, we need to express 0.001 as a power of 10. 0.001 can be written as 1/1000, which can be further written as 10^-3 because 10^-3 is the reciprocal of 10^3.

With this understanding, we now have 10^x = 10^-3.

Since the bases are the same on both sides (both are 10), we can equate the exponents: x = -3.

Therefore, log0.001 (base 10) = -3.