/*! 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 35 Find each logarithm. Round to si... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 35

Find each logarithm. Round to six decimal places. $$\ln 5894$$

Short Answer

Expert verified
The natural logarithm of 5894 is approximately 8.681765.

Step by step solution

01

Understand the Logarithm Function

The natural logarithm function, denoted as \(\backslashln\), is the logarithm to the base \(\backslasheln\). It is used to determine the power to which the base e must be raised to obtain a given number.
02

Use a Calculator

To find \(\backslashln 5894\), use a scientific calculator, which typically has a \(\backslashln\) button. Enter the number 5894 and press the \(\backslashln\) button to get the result.
03

Read the Result

The calculator will display the natural logarithm of 5894 as \(\backslashln 5894 \approx 8.681765\). Ensure to round the result to six decimal places.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

logarithm function
Unlike common logarithms (base 10), the natural logarithm is primarily used in higher mathematics, such as calculus and complex variable analysis. Its applications are widespread, including solving equations in engineering and physics.
Understanding the foundational idea behind logarithms is crucial as it allows us to transform multiplicative processes into additive ones, simplifying many complex problems.
scientific calculator
It's important to ensure that the number is entered correctly to get an accurate result.
For more advanced calculations, scientific calculators offer other functions such as exponentiation, trigonometry, and statistical operations. Familiarizing oneself with these features can enhance problem-solving efficiency in various mathematical domains.
rounding numbers
To round to six decimal places, we look at the seventh decimal place. If the seventh decimal is 5 or greater, we round up the sixth decimal by one. If it is less than 5, we leave the sixth decimal as is. In this example, \( \text{ln} \, 5894 \) already ends exactly at the sixth decimal place, avoiding any rounding issues.
Mastering the concept of rounding helps in checking the precision of your results and ensures consistency across various calculations and studies.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Differentiate. $$g(x)=-\log _{6}(\sqrt[3]{x}+5)$$

Find the minimum value of each function. Use a graphing calculator, iPlot, or Graphicus. $$f(x)=x^{2} \ln x$$

Find an expression relating the exponential growth rate \(k\) and the tripling time \(T_{3}\).

Differentiate. $$f(x)=\ln \left(x^{3}+1\right)^{5}$$

Differentiate. $$y=e^{8 x}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.