Math Problem Statement
Evaluate without using a calculator.
log Subscript 10 Baseline 1000
Solution
To evaluate without using a calculator, follow these steps:
- Recall that represents the exponent to which the base 10 must be raised to produce .
- We know that can be written as a power of 10:
- Therefore, asks, "To what power must 10 be raised to get 1000?"
- Since , the answer is:
So, .
Would you like more details or have any questions about this? Here are some related questions you might consider:
- How do you evaluate without using a calculator?
- What is and how can it be evaluated without a calculator?
- How can the properties of logarithms simplify the evaluation of expressions like ?
- How do logarithmic functions relate to exponential functions?
- What is the general form for solving when and 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