/*! 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 121 Explain how to solve an exponent... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 121

Explain how to solve an exponential equation when both sides can be written as a power of the same base.

Short Answer

Expert verified
For exponential equations where both sides have a common base, simplify the equation by setting the exponents equal to each other and then solve for the variable. For instance, in the equation \(2^{3x} = 2^{7}\) after equating the exponents we obtain \(3x = 7\), and therefore \(x = 7/3\).

Step by step solution

01

Identification

Understand the question and identify the exponential equations where both sides can be written as a power of the same base. Let's consider an example for better understanding: \(2^{3x} = 2^{7}\). Here, \(2^{3x}\) and \(2^{7}\) are exponential notations where both sides can be written as a power of same base, which is 2.
02

Reduce to Common Base

When the bases are equal, we can equate exponents. Here, because both terms have a base of 2, the equation is simplified and we get: \(3x = 7\).
03

Solve for the variable

We have a linear equation at this stage, which we can solve using elementary algebra. Divide both sides of the equation by 3 to isolate x: \(x = 7/3\).

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

Logarithmic models are well suited to phenomena in which growth is initially rapid but then begins to level off. Describe something that is changing over time that can be modeled using a logarithmic function.

Research applications of logarithmic functions as mathematical models and plan a seminar based on your group's research. Each group member should research one of the following areas or any other area of interest: \(\mathrm{pH}\) (acidity of solutions), intensity of sound (decibels), brightness of stars, human memory, progress over time in a sport, profit over time. For the area that you select, explain how logarithmic functions are used and provide examples.

Solve each equation. Check each proposed solution by direct substitution or with a graphing utility. $$ \ln (\ln x)=0 $$

Explain why the logarithm of 1 with base \(b\) is \(0 .\)

Find the domain of each logarithmic function. $$ f(x)=\log \left(\frac{x+1}{x-5}\right) $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.