log 1/1000 = -3
-3 = 1/1000
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The statement “log 1/1000 = -3” is correct because the logarithm base 10 of 1/1000 is indeed -3. This is due to the fact that 10 raised to the power of -3 equals 1/1000.
Here’s a short breakdown:
1. Understanding Logarithms: The logarithm log_b(a) answers the question, “To what power must the base b be raised to obtain a?” So in log 1/1000 = -3, we’re asking: “10 raised to what power gives us 1/1000?”
2. Calculating the Power: We know that:
[
10^{-3} = frac{1}{10^3} = frac{1}{1000}
]
Thus, log 1/1000 = -3.
3. Reiteration: Therefore, -3 = log(1/1000), confirming that the logarithm expresses the relationship between the base and its exponential form.
If you have any more questions or need further clarification, feel free to ask!