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Chapter 12: Problem 17

Find logarithm. Give approximations to four decimal places. \(\ln 0.0556\)

Short Answer

Expert verified
-2.8904

Step by step solution

01

- Understanding the Natural Logarithm

The natural logarithm, denoted as \( \ln \ \), is the logarithm to the base \( \text{e} \ \) (where e is approximately equal to 2.718281828). It is often required to find the natural logarithm of a given number.
02

- Using a Calculator

To find the natural logarithm of 0.0556, use a scientific calculator. Input \( \ln(0.0556) \ \) into the calculator to get the value. Make sure your calculator is set to evaluate natural logarithms.
03

- Approximate to Four Decimal Places

After calculating using the calculator, note the full result. Here, \( \ln(0.0556) 鈮� -2.890371757 \ \). Now round this value to four decimal places: \( \ln(0.0556) 鈮� -2.8904 \ \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Logarithms
Logarithms are a fundamental concept in mathematics, providing a way to measure the magnitude of numbers on a different scale. Instead of thinking in terms of multiplication, they help us understand exponential relationships. There are different types of logarithms, but the most common in higher-level math are the common logarithm (base 10) and the natural logarithm (base e). The natural logarithm, denoted as \(\text{ln}\), particularly helps in scenarios involving growth and decay processes, such as population models and radioactive decay.
Using a Scientific Calculator
Understanding how to use a scientific calculator is crucial for solving logarithmic problems. A scientific calculator is designed to handle functions beyond simple arithmetic, including logarithms. To find the natural logarithm of a number, such as 0.0556, ensure your calculator is in the mode to compute natural logarithms by locating the button labeled 'LN' or 'ln'. Enter the value 0.0556 and then press the 'LN' button. This will provide the logarithmic value. For example, when computing \(\text{ln}(0.0556)\), your calculator should output approximately -2.890371757.
Rounding
Rounding is an essential skill in mathematics, enabling us to simplify numbers while maintaining a certain degree of accuracy. When dealing with logarithmic results, it鈥檚 often required to present the value in a more manageable form by rounding to a specific number of decimal places. For instance, if the calculated value of \(\text{ln}(0.0556)\) is approximately -2.890371757, you may need to round it to four decimal places for practical purposes. To do this, look at the fifth decimal place. If it is 5 or higher, round up; if it is less than 5, round down. Thus, -2.890371757 rounds to -2.8904.

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Most popular questions from this chapter

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