Math Problem Statement

Evaluate the following using a calculator.

​(A) log 3 comma 383.3log3,383.3

​(B) log 0.0882595log0.0882595

​(C) ln 444.22ln444.22

​(D) ln 0.042449

Solution

import math

Evaluating the logarithmic and natural logarithmic expressions

log_A = math.log10(3383.3) log_B = math.log10(0.0882595) ln_C = math.log(444.22) ln_D = math.log(0.042449)

log_A, log_B, ln_C, ln_DHere are the evaluations:

  • (A) log(3383.3)3.5293\log(3383.3) \approx 3.5293
  • (B) log(0.0882595)1.0542\log(0.0882595) \approx -1.0542
  • (C) ln(444.22)6.0963\ln(444.22) \approx 6.0963
  • (D) ln(0.042449)3.1595\ln(0.042449) \approx -3.1595

Would you like further details or explanations on these calculations?

Here are 5 related questions:

  1. How do logarithms with different bases relate to each other?
  2. What are some real-life applications of logarithmic functions?
  3. How does the logarithmic scale work, particularly in measuring sound intensity?
  4. What are the properties of natural logarithms (ln\ln) and how are they used in calculus?
  5. How do you solve equations involving logarithms?

Tip: Remember that the logarithm of a number less than 1 will yield a negative result, while the logarithm of a number greater than 1 will be positive.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Natural Logarithms

Formulas

logarithm base 10 (log)
natural logarithm (ln)

Theorems

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Suitable Grade Level

Advanced High School