What is log 1000?
Understand the Problem
The question is asking for the logarithm of 1000. This involves determining the exponent to which a number (usually 10 or e) must be raised to yield 1000.
Answer
$3$
Answer for screen readers
The answer is $3$.
Steps to Solve
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Identify the logarithm base In this case, we will consider the common logarithm, which has a base of 10. We want to find $\log_{10}(1000)$.
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Rewrite 1000 as a power of 10 To make calculations easier, we can express 1000 as a power of 10. We know that: $$ 1000 = 10^3 $$
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Apply the logarithmic identity Using the property of logarithms that states $\log_{b}(b^x) = x$, we can apply this here: $$ \log_{10}(1000) = \log_{10}(10^3) $$
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Simplify to find the logarithm Now, we can simplify it using our identity: $$ \log_{10}(10^3) = 3 $$
The answer is $3$.
More Information
This means that 10 raised to the power of 3 equals 1000. The logarithm helps us find out how many times we need to multiply 10 by itself to get 1000.
Tips
- Confusing the base of the logarithm: Always ensure you know the base of the logarithm you're working with; in this case, it is base 10.
- Misidentifying the exponent when rewriting numbers: It's important to carefully check how numbers can be expressed as powers.
