Math Problem Statement

Use a calculator to find the common logarithm. log(14.3).

Solution

To solve the problem in the image, you need to calculate the common logarithm log(14.3)\log(14.3), which uses base 10.

Using a calculator:

log(14.3)1.1553\log(14.3) \approx 1.1553

The result rounded to four decimal places is:

1.1553\boxed{1.1553}

Would you like a detailed explanation of logarithms or how to calculate this manually? Let me know if you have any additional questions!

Questions to expand on this:

  1. What are the properties of logarithms, and how are they applied in problems like this?
  2. How is the common logarithm different from the natural logarithm?
  3. Why is it important to round logarithmic values to a specific decimal place?
  4. How do calculators compute logarithms internally?
  5. What are some practical applications of common logarithms in science or engineering?

Tip:

When solving logarithmic problems, always double-check your calculator mode to ensure accuracy, especially when working with multiple bases.

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Math Problem Analysis

Mathematical Concepts

Common Logarithms
Base 10 Logarithms
Rounding Numbers

Formulas

log_b(x) = y, where b^y = x and b is the base (here, b = 10)

Theorems

Logarithmic Properties: Change of Base Formula, Exponent-Log Relationship

Suitable Grade Level

Grades 9-12