/*! 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 6 In Exercises \(1-40,\) use prope... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 6

In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log (10,000 x) $$

Short Answer

Expert verified
The expanded form of \(\log (10,000 x)\) is \(4 + \log x\).

Step by step solution

01

Break Down the Expression

First, the expression needs to be separated according to the product rule of logarithms, which states that \(\log_b(mn) = \log_b m + \log_b n\). Here, \(m=10000\) and \(n=x\), thus the expression \(\log (10,000x)\) can be rewritten as \(\log 10000 + \log x\).
02

Evaluate the Logarithm

Next, we evaluate the \(\log 10000\) portion of the expression. In the context of common logarithms (base 10), \(\log 10000 = \log 10^4\), and using the rule \(\log_b b^a = a\), we have \(\log 10^4 = 4\). So, the expression \(\log 10000 + \log x\) becomes \(4 + \log x\).
03

Finalize the Expression

Lastly, the unaltered portion of the initial expression, \(\log x\), remains in the final expression as-is because there's no further simplification possible without knowing the value of \(x\). Thus, the final expanded form of the expression is \(4 + \log x\).

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

In Exercises \(71-78,\) use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$ \log _{16} 57,2 $$

In Exercises \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ \frac{1}{5}\left(\log _{4} x-\log _{4} y\right)+2 \log _{4}(x+1) $$

In Exercises \(71-78,\) use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$ \log _{0.1} 17 $$

In Exercises \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ 2 \ln x-\frac{1}{2} \ln y $$

In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log _{9}(9 x) $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

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.