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Chapter 4: Problem 82

Evaluate or simplify each expression without using a calculator. $$\log 1000$$

Short Answer

Expert verified
The simplified value of \(\log 1000\) is 3

Step by step solution

01

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).
02

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.

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Most popular questions from this chapter

Complete the table for a savings account subject to contimuous compounding ( \(A=P e^{n}\) ). Round answers to one decimal place. Amount Invested 8000 dollar Annual Interest Rate 8% Accumulated Amount Double the amount invested Time \(t\) in Years _______

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