/*! 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 66 Write the exponential equation i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 66

Write the exponential equation in logarithmic form. $$e^{2 x}=3$$

Short Answer

Expert verified
The exponential equation \(e^{2x} = 3\) can be written in logarithmic form as \(ln(3) = 2x\).

Step by step solution

01

Understand the Components of the Exponential Equation

An exponential equation typically takes the form \(base^{exponent} = result\). Here, we have \(e^{2x} = 3\), where 'e' is the base, '2x' is the exponent, and '3' is the result.
02

Write the Equation in Logarithmic Form

In logarithmic form, we rearrange the components to take the form \(\log_{base}(result) = exponent\). Therefore, the equation \(e^{2x} = 3\) is written in logarithmic form as \(\log_{e}(3) = 2x\).
03

Simplifying the Logarithmic Form

The base 'e' denotes the natural logarithm, more commonly written as 'ln'. Therefore, we can write the equation as \(ln(3) = 2x\).

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

Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$2 \ln (x+3)=3$$

The populations \(P\) (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by \(P=\frac{2632}{1+0.083 e^{0.0500 t}}\) where \(t\) represents the year, with \(t=0\) corresponding to \(2000 .\) (Source: U.S. Census Bureau) (a) Use the model to find the populations of Pittsburgh in the years \(2000,2005,\) and 2007 . (b) Use a graphing utility to graph the function. (c) Use the graph to determine the year in which the population will reach 2.2 million. (d) Confirm your answer to part (c) algebraically.

In a group project in learning theory, a mathematical model for the proportion \(P\) of correct responses after \(n\) trials was found to be \(P=0.83 /\left(1+e^{-0.2 n}\right)\) (a) Use a graphing utility to graph the function. (b) Use the graph to determine any horizontal asymptotes of the graph of the function. Interpret the meaning of the upper asymptote in the context of this problem. (c) After how many trials will \(60 \%\) of the responses be correct?

Solve the equation algebraically. Round the result to three decimal places. Verify your answer using a graphing utility. $$2 x^{2} e^{2 x}+2 x e^{2 x}=0$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log 8 x-\log (1+\sqrt{x})=2$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Decision 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.