/*! 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 24 In Exercises \(1-40,\) use prope... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 24

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. $$ \log _{5}\left(\frac{\sqrt{x}}{25}\right) $$

Short Answer

Expert verified
The expanded and simplified form of the given logarithmic expression is \(\frac{1}{2} \log _{5} x - 2\).

Step by step solution

01

Applying the quotient rule

The quotient rule states that \(\log_b\frac{m}{n} = \log_b m - \log_b n\). Hence the given expression can be rewritten as: \[\log _{5}(\sqrt{x})-\log _{5}(25)\]
02

Apply the power rule

The power rule states that \(\log_b m^n = n \log_b m\). Applying the power rule to our expression, we have: \[\frac{1}{2}\log _{5} x - \log _{5} (5^2)\]. Notice that, in the second part of the expression, we apply the power rule with a power of 2.
03

Simplify the expression

We know that \(\log_b b^p = p\). So, \(\log _{5} 5^2 = 2\). Substitute this back into the expression to get the simplified version: \[\frac{1}{2}\log _{5} x - 2\]

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 \(41-70\), 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. $$ \log x+\log 15+\log \left(x^{2}-4\right)-\log (x+2) $$

Write as a single term that does not contain a logarithm: $$ e^{\ln 8 x^{4}-\ln 2 x^{2}} $$

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

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. $$ \log _{3} 405-\log _{3} 5 $$

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. $$ \log \left[\frac{10 x^{2} \sqrt[3]{1-x}}{7(x+1)^{2}}\right] $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.