Math Problem Statement

what is the value of log(1,000)

Solution

The expression log(1000)\log(1000) is typically assumed to be a common logarithm, which means it's using base 10. In other words, you're looking for the exponent to which 1010 must be raised to get 10001000.

We can express 10001000 as a power of 1010:

1000=1031000 = 10^3

So:

log10(1000)=3\log_{10}(1000) = 3

Thus, log(1000)=3\log(1000) = 3.

Would you like more details on logarithms or have any questions?


Here are some related questions:

  1. What is the value of log(100)\log(100)?
  2. How do you express log10(0.01)\log_{10}(0.01) in exponential form?
  3. What is the value of log2(32)\log_{2}(32)?
  4. Can you explain the difference between natural logarithms and common logarithms?
  5. How do you calculate logarithms for non-integer values?
  6. What is the value of log10(1)\log_{10}(1)?
  7. How do you solve logarithmic equations with different bases?
  8. What is the significance of the logarithmic scale in real-world applications?

Tip: The common logarithm, denoted as log(x)\log(x), assumes a base of 10. This is widely used in scientific calculations and for working with large numbers.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponential Functions

Formulas

\(\log_b(a) = c\) implies \(b^c = a\)

Theorems

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Suitable Grade Level

High School