Math Problem Statement

Evaluate without using a calculator.

log Subscript 10 Baseline 1000

Solution

To evaluate log101000\log_{10} 1000 without using a calculator, follow these steps:

  1. Recall that log10x\log_{10} x represents the exponent to which the base 10 must be raised to produce xx.
  2. We know that 10001000 can be written as a power of 10:
    1000=1031000 = 10^3
  3. Therefore, log101000\log_{10} 1000 asks, "To what power must 10 be raised to get 1000?"
  4. Since 103=100010^3 = 1000, the answer is: log101000=3\log_{10} 1000 = 3

So, log101000=3\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 log10100\log_{10} 100 without using a calculator?
  2. What is log28\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 log100.01\log_{10} 0.01?
  4. How do logarithmic functions relate to exponential functions?
  5. What is the general form for solving logb(x)=y\log_b(x) = y when bb and yy 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.

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Math Problem Analysis

Mathematical Concepts

Logarithms

Formulas

\( \log_b(x) \) definition

Theorems

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Suitable Grade Level

Grades 10-12