/*! 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 144 Without using a calculator, find... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 144

Without using a calculator, find the exact value of \(\log _{4}\left[\log _{3}\left(\log _{2} 8\right)\right]\)

Short Answer

Expert verified
The exact value of the given logarithmic expression is \(0\).

Step by step solution

01

Evaluating \( \log_{2}(8) \)

We start by evaluating the innermost logarithm \(\log_{2}(8)\). Since \(2^{3} = 8\), we know that \(\log_{2}(8) = 3\). Thus the original expression becomes \(\log_{4}[\log_{3}(3)]\).
02

Evaluating \( \log_{3}(3) \)

Next we evaluate \(\log_{3}(3)\). Since \(3^{1} = 3\), we know that \(\log_{3}(3) = 1\). Therefore, the original expression now simplifies to \(\log_{4}(1)\).
03

Evaluating \( \log_{4}(1) \)

Finally, we evaluate \(\log_{4}(1)\). Since \(4^{0} = 1\), we know that \(\log_{4}(1) = 0\). Hence, the original expression simplifies to 0 as its ultimate value.

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

Solve the equation \(x^{3}-9 x^{2}+26 x-24=0\) given that 4 is a zero of \(f(x)=x^{3}-9 x^{2}+26 x-24\) Example \(6)\)

Check each proposed solution by direct substitution or with a graphing utility. $$ (\log x)(2 \log x+1)=6 $$

Three of the richest comedians in the United States are Larry David (creator of Seinfeld), Matt Groening (creator of The Simpsons), and Trey Parker (co- creator of South Park). Larry David is worth \(\$ 450\) million more than Trey Parker. Matt Groening is worth \(\$ 150\) million more than Trey Parker. Combined, the net worth of these three comedians is \(\$ 1650\) million (or \(\$ 16.5\) billion). Determine how much, in millions of dollars, each of these comedians is worth. (Source: petamovies.com) (Section 1.3, Example 1)

Exercises 150鈥�152 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: \(\log _{2} 16\) b. Evaluate: \(\log _{2} 32-\log _{2} 2\) c. What can you conclude about $$ \log _{2} 16, \text { or } \log _{2}\left(\frac{32}{2}\right) ? $$

Describe the change-of-base property and give an example.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.