Evaluate without using a calculator.

log Subscript 10 Baseline 1000

To evaluate \( \log_{10} 1000 \) without using a calculator, follow these steps:

1. Recall that \( \log_{10} x \) represents the exponent to which the base 10 must be raised to produce \( x \).
2. We know that \( 1000 \) can be written as a power of 10:  
   \[
   1000 = 10^3
   \]
3. Therefore, \( \log_{10} 1000 \) asks, "To what power must 10 be raised to get 1000?"
4. Since \( 10^3 = 1000 \), the answer is:
   \[
   \log_{10} 1000 = 3
   \]

So, \( \log_{10} 1000 = 3 \).

Would you like more details or have any questions about this? Here are some related questions you might consider:

1. How do you evaluate \( \log_{10} 100 \) without using a calculator?
2. What is \( \log_{2} 8 \) and how can it be evaluated without a calculator?
3. How can the properties of logarithms simplify the evaluation of expressions like \( \log_{10} 0.01 \)?
4. How do logarithmic functions relate to exponential functions?
5. What is the general form for solving \( \log_b(x) = y \) when \( b \) and \( y \) are known?

**Tip:** When evaluating logarithms, always check if the argument can be expressed as a power of the base. This simplifies the calculation significantly.

Learn how to evaluate \( \log_{10} 1000 \) without using a calculator with a detailed step-by-step explanation. This problem covers logarithmic concepts, including the definition of logarithms and properties of exponents. Suitable for students in Grades 10-12.

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