/*! 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 107 Describe the power rule for loga... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 107

Describe the power rule for logarithms and give an example.

Short Answer

Expert verified
The power rule for logarithms states that \( \log_b (b^n) = n \cdot \log_b (b) \). For example, \( \log_2 (2^3) \) simplifies to 3.

Step by step solution

01

Defining the Power Rule for Logarithms

The power rule for logarithms states that for any real numbers \( b \) and \( x \), and integer \( n \), the logarithm of \( b^n \) can be written as the product of \( n \) and the logarithm of \( b \). Formally, this is: \( \log_b (b^n) = n \cdot \log_b (b) \)
02

Example of Applying the Power Rule for Logarithms

As a practical example, consider \( \log_2 (2^3) \). Using the power rule for logarithms, this expression simplifies to \( 3 \cdot \log_2 (2) \). Since the log base 2 of 2 is 1, the final answer is \( 3 \cdot 1 = 3 \).

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

Given \(f(x)=\frac{2}{x+1}\) and \(g(x)=\frac{1}{x},\) find each of the following: a. \((f \circ g)(x)\) b. the domain of \(f \circ g\) (Section \(2.6, \text { Example } 6)\)

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. $$ 3^{x}=2 x+3 $$

In Example I on page \(520,\) we used two data points and an exponential function to model the population of the United States from 1970 through 2010 . The data are shown again in the table. Use all five data points to solve Exercises \(66-70\). $$ \begin{array}{cc} {x, \text { Number of Years }} & {y, \text { U.S. Population }} \\ {\text { after } 1969} & {\text { (millions) }} \\ {1(1970)} & {203.3} \\ {11(1980)} & {226.5} \\ {21(1990)} & {248.7} \\ {31(2000)} & {281.4} \\ {41(2010)} & {308.7} \end{array} $$ Use your graphing utility's power regression option to obtain a model of the form \(y=a x^{b}\) that fits the data. How well does the correlation coefficient, \(r,\) indicate that the model fits the data?

Exercises \(86-88\) will help you prepare for the material covered in the first section of the next chapter. $$ \text { Simplify: } \frac{17 \pi}{6}-2 \pi $$

Find \(\ln 2\) using a calculator. Then calculate each of the following: \(1-\frac{1}{2} ; \quad 1-\frac{1}{2}+\frac{1}{3} ; \quad 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\) \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5} ; \ldots\) Describe what you observe.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Pure 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.