Problem 82
Question
Evaluate or simplify each expression without using a calculator. $$\log 1000$$
Step-by-Step Solution
Verified Answer
The simplified value of \(\log 1000\) is 3
1Step 1: Understanding Logarithms
When we read \(\log 1000\), it's the same as saying '10 to the power of what number equals 1000'. This is based on the definition that \(\log_b a = x\) means \(b^x = a\). In this case, 'b' is 10 (our base), 'a' is 1000 (the number we're trying to find the logarithm of), and 'x' is the unknown (the power we're trying to find).
2Step 2: Simplifying Expression
1000 is \(10^3\), hence \(\log 1000\) is equal to 3 since 10 raised to the power of 3 gives 1000 based on the logarithm definition.
Other exercises in this chapter
Problem 81
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