/*! 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 3: Problem 110

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

Short Answer

Expert verified
The short answer is the result obtained after completing the calculation in step 3. The exact value may vary depending on the precision of the calculator used but should be around 2.36.

Step by step solution

01

Understanding The Change of Base Formula

The change of base formula is a mathematical rule that allows one to compute the logarithm of any number, using any base, when a calculator with only log base 10 (or base e) is available. The formula is as follows: \(\log_b a = \frac{\log_c a}{\log_c b}\). The base 'c' can actually be any positive number (except 1), but is most commonly either 10 or e since these are common logarithm forms on calculators.
02

Applying the Formula to the Given Problem

Applying the change of base formula to this exercise means expressing the logarithm base 14 of 283 as the division of the logarithm (in base 10 or e) of 283 and 14. Like this: \(\log _{14} 283 = \frac{\log_{10} 283}{\log_{10} 14} \).
03

Calculating the Logs using a calculator

In this step, a calculator is used to calculate both of the logs in step 2. Calculators typically have a log button that calculates base 10 logs. Calculate log of 283 and log of 14 separately, then divide the result of log(283) by the result of log(14).
04

Final Answer

The result of the calculation in step 3 is the answer to the problem.

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

Rewrite the equation in terms of base \(e\). Express the answer in terms of a natural logarithm and then round to three decimal places. $$y=2.5(0.7)^{x}$$

In \(1626,\) Peter Minuit convinced the Wappinger Indians to sell him Manhattan Island for \(\$ 24 .\) If the Native Americans had put the \(\$ 24\) into a bank account paying \(5 \%\) interest, how much would the investment have been worth in the year 2010 if interest were compounded a. monthly? b. continuously?

$$\text { Solve for } y: 7 x+3 y=18$$

In Exercises \(125-132,\) use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set. Verify this value by direct substitution into the equation. $$\log (x+3)+\log x=1$$

Without using a calculator, find the exact value of $$ \frac{\log _{3} 81-\log _{\pi} 1}{\log _{2 \sqrt{2}} 8-\log 0.001} $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

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.