Math Problem Statement

what is the log of 48

Solution

The logarithm of a number depends on the base you are using. By default, logarithms are often calculated in base 10 (common logarithm, denoted as log10\log_{10}) or base ee (natural logarithm, denoted as ln\ln).

  1. Common Logarithm (log10(48)\log_{10}(48)): log10(48)1.68124\log_{10}(48) \approx 1.68124

  2. Natural Logarithm (ln(48)\ln(48)): ln(48)3.8712\ln(48) \approx 3.8712

If you need the logarithm in a different base, the formula is: logb(x)=log10(x)log10(b)\log_b(x) = \frac{\log_{10}(x)}{\log_{10}(b)}

Would you like further details or help with specific calculations? 😊

Here are 5 related questions:

  1. How is the logarithm of a number calculated without a calculator?
  2. What is the logarithm of 48 in base 2?
  3. Can you show the relationship between ln(x)\ln(x) and log10(x)\log_{10}(x)?
  4. How is the change-of-base formula for logarithms derived?
  5. What are the practical applications of logarithms in real-life problems?

Tip: The natural logarithm (ln\ln) is commonly used in problems involving growth and decay, especially in sciences and engineering.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Bases of logarithms (base 10, base e)
Change of base formula

Formulas

Common logarithm: log10(x)
Natural logarithm: ln(x)
Change of base formula: log_b(x) = log10(x) / log10(b)

Theorems

Logarithmic properties
Change of base theorem

Suitable Grade Level

Grades 9-12