/*! 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 110 Explain how to use your calculat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 110

Explain how to use your calculator to find \(\log _{14} 283\)

Short Answer

Expert verified
To find \(\log _{14} 283\), use the change of base formula. Thus, \(\log _{14} 283 = \frac{\log 283}{\log 14}\). Use your calculator to find the values of \(\log 283\) and \(\log 14\), and divide the first result by the second one.

Step by step solution

01

Understand the problem

To find \(\log _{14} 283\), we need to know what power we have to raise 14 to get 283. However, our calculator only provides log base 10 or natural log (base e). The problem thus lies in translating our base-14 logarithm into a form which the calculator can comprehend.
02

Use the change of base formula

The change of base formula is \(\log_b a = \frac{\log_d a}{\log_d b}\). We can use this to translate \(\log _{14} 283\) into \(\frac{\log 283}{\log 14}\). This is now an equation that your calculator can understand.
03

Use your calculator

Now that we have \(\frac{\log 283}{\log 14}\), we can use your calculator to work this out. First, calculate \(\log 283\), then calculate \(\log 14\), and finally divide the first result with the second one.

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!

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

Write as a single term that does not contain a logarithm: \(e^{\ln 8 x^{3}-\ln 2 x^{2}}\)

Explain why the logarithm of 1 with base \(b\) is \(0 .\)

Will help you prepare for the material covered in the next section. In each exercise, evaluate the indicated logarithmic expressions without using a calculator. a. Evaluate: \(\log _{2} 32\) b. Evaluate: \(\log _{2} 8+\log _{2} 4\) c. What can you conclude about \(\log _{2} 32,\) or \(\log _{2}(8 \cdot 4) ?\)

Write each equation in its equivalent exponential form. Then solve for \(x .\) $$ \log _{4} x=-3 $$

In Exercises \(125-128,\) determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ \ln \sqrt{2}=\frac{\ln 2}{2} $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Calculus

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.