Math Problem Statement

log 0.48 = ?

Solution

The image shows the logarithmic expression:

log0.48=?\log 0.48 = \,?

The logarithm without a base explicitly mentioned is generally assumed to be base 10, meaning we need to calculate:

log10(0.48)\log_{10}(0.48)

Using a calculator, the value of log10(0.48)\log_{10}(0.48) is approximately:

log10(0.48)0.3188\log_{10}(0.48) \approx -0.3188

This is the solution to the logarithmic expression.

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

Here are 5 related questions you might explore:

  1. What is log10(1)\log_{10}(1)?
  2. How do you calculate log10(0.75)\log_{10}(0.75)?
  3. Can you explain the difference between natural logarithms and common logarithms?
  4. What is the value of log10(10)\log_{10}(10)?
  5. How can you express log10(x)=y\log_{10}(x) = y in exponential form?

Tip: Negative values in logarithms occur when the argument (inside the logarithm) is between 0 and 1.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Base-10 Logarithm
Properties of Logarithms

Formulas

log_b(x) = y, where b^y = x

Theorems

Logarithmic properties: log(ab) = log(a) + log(b) and log(a/b) = log(a) - log(b)

Suitable Grade Level

Grades 9-12