/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 65 Find the following using a calcu... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 65

Find the following using a calculator. Round to four decimal places. $$\ln 809.3$$

Short Answer

Expert verified
6.6967

Step by step solution

01

- Understanding the logarithm function

The natural logarithm function, denoted as \( \ln \), is the inverse of the exponential function with base \(e\). This means that \( \ln (x) \) is the power to which \(e\) must be raised to get \(x\).
02

- Using the calculator

To find \( \ln (809.3) \) using a calculator, locate the \( \ln\) button. Enter \809.3\ and then press the \ln\ button.
03

- Reading the result

After pressing the \( \ln \) button, the calculator will display the natural logarithm of \(809.3\). The result should be rounded to four decimal places.
04

- Rounding the answer

If the calculator shows more than four decimal places, round the result to the nearest four decimal places.

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Key Concepts

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

inverse exponential function
The natural logarithm function (\(\ln\)) and the exponential function with base \(e\) are inverses of each other.
This means that if you have \(e^{y} = x\), then \(\ln(x) = y\).
In other words, the natural logarithm of a number \(x\) gives the power to which \(e\) must be raised to equal \(x\).
This property is especially useful in many aspects of science and engineering because it allows us to solve for variables that are in the exponent.
When you understand this inverse relationship, calculating logarithms becomes much more intuitive.
For instance, calculating \(\ln(809.3)\) will tell us the power to which \(e\) needs to be raised in order to get \(809.3\).
calculating logarithms
Calculating logarithms, especially natural logarithms, can be easily done with a calculator.
Here are the steps you can follow when calculating \(\ln(809.3)\):
  • Locate the \(\ln\) button on your calculator. It is usually among the scientific functions.
  • Enter the number for which you want to find the natural logarithm, in this case, 809.3.
  • Press the \(\ln\) button. The calculator will display the calculated logarithm value.

Practice calculating natural logarithms with different values to become more familiar with the process and to improve your understanding of this useful mathematical function.
rounding numbers
Rounding is an essential skill for presenting numbers in a clean and comprehensible manner.
When a calculation results in a long decimal, you often need to round to a set number of decimal places.
Here's a quick guide to rounding to four decimal places:
  • Identify the digit in the fourth decimal place.
  • Look at the digit immediately to the right (the fifth decimal place).
  • If this digit is 5 or higher, round up by adding 1 to the fourth decimal place digit.
  • If this digit is 4 or lower, keep the fourth decimal place digit unchanged.

For example, if your calculator shows \(\ln(809.3) = 6.694891\), then the rounded result to four decimal places would be \(6.6949\).

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Most popular questions from this chapter

Use a graphing calculator to find the approximate solutions of the equation. $$0.082 e^{0.05 x}=0.034$$

Use a graphing calculator to find the point \((s)\) of intersection of the graphs of each of the following pairs of equations. $$y=\frac{1}{e^{x}+1}, y=0.3 x+\frac{7}{9}$$

Solve. $$2^{x^{2}-9 x}=\frac{1}{256}$$

Solve using any method. $$x\left(\ln \frac{1}{6}\right)=\ln 6$$

Using only a graphing calculator, determine whether the functions are inverses of each other. $$f(x)=\sqrt[3]{\frac{x-3.2}{1.4}}, g(x)=1.4 x^{3}+3.2$$
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