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Chapter 4: Problem 29

$$ \text { Find the logarithm. Round to six decimal places } $$ $$ \text { ln } 3927 $$

Short Answer

Expert verified
8.274302

Step by step solution

01

Understand the Logarithm

The natural logarithm (ln) refers to the logarithm to the base e, where e is approximately 2.71828. The natural logarithm function, ln(x), gives the power to which e must be raised to get x.
02

Use a Calculator

To find the natural logarithm of 3927, use a scientific calculator or a mathematical tool that can compute natural logarithms. Enter 3927 and apply the natural logarithm (ln) function.
03

Record the Result

After applying the natural logarithm function to 3927, the calculator should display a value. Ensure this value is rounded to six decimal places.
04

Round the Value

When rounded to six decimal places, the natural logarithm of 3927 is approximately 8.274302.

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Key Concepts

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

Understanding Logarithms
Logarithms, including the natural logarithm (ln), are mathematical functions that help us solve problems involving exponential growth or decay. When we talk about the natural logarithm, ln, it means that we are working with a logarithm that has the base e. The number e is a special irrational number approximately equal to 2.71828. Essentially, the natural logarithm of a number tells us the power to which e must be raised to get that number. For example, when we calculate ln(3927), we find the exponent that makes the equation e^x = 3927 true.
Rounding Numbers
Rounding numbers is a common practice to simplify results for practical use. When you're asked to round to a specific number of decimal places, follow these general rules:
  • Identify the digit at the place you're asked to round to.
  • Look at the digit immediately to the right of this place.
  • If this digit is 5 or higher, increase your identified digit by one.
  • If this digit is 4 or lower, keep your identified digit the same.
Applying these rules, we can round the natural logarithm of 3927 to six decimal places. If the calculated value is, for instance, 8.2743017, we round it to 8.274302 because the seventh digit is 7, which is greater than 5.
Using Scientific Calculators
Scientific calculators are powerful tools that can help you solve complex mathematical problems, including finding logarithms. Follow these steps to use a scientific calculator to find the natural logarithm:
  • Turn on the calculator and make sure it is set to the correct mode (usually this will be 'normal' mode).
  • Enter the number for which you need the natural logarithm. In this case, you would type in 3927.
  • Press the 'ln' button on the calculator. This button tells the calculator to compute the natural logarithm of the entered number.
  • Read the displayed result and ensure you record it correctly.
Advanced calculators might also allow you to directly input expressions. Make sure always to check your calculator's manual if unsure. This process helps to ensure that you can find natural logarithms quickly and accurately.

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Most popular questions from this chapter

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