/*! 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 58 Rewrite the equation in terms of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 58

Rewrite the equation in terms of base \(e\). Express the answer in terms of a natural logarithm and then round to three decimal places. $$y=1000(7.3)^{x}$$

Short Answer

Expert verified
The equation, in terms of base e, rounded to three decimal places, is \(x = (\ln y - \ln(1000))/ \ln(7.3)\)

Step by step solution

01

Rewrite the Equation

The given equation is \(y=1000(7.3)^{x}\). This can be rewritten in terms of base \(e\) by taking natural logs on both sides. Remembering that \(\ln(ab) = \ln(a) + \ln(b)\) and \(\ln(a^b) = b*\ln(a)\), the equation becomes \(\ln y = \ln(1000) + \ln((7.3)^x)\). This step utilizes the properties of logarithms to simplify the equation.
02

Simplify the Equation

Continue to simplify the equation, remembering that \(\ln(a^b) = b*\ln(a)\), so \(\ln((7.3)^x) = x * \ln(7.3)\). Then, the equation becomes \(\ln y = \ln(1000) + x*\ln(7.3)\).
03

Express the Equation in Terms of x

Express the equation in terms of x, this would give a final equation of: \(x = (\ln y - \ln(1000))/ \ln(7.3)\)

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

Solve and graph the solution set on a number line: \(2 x^{2}+5 x<12 .\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I used an exponential function to model Russia's declining population, the growth rate \(k\) was negative.

Begin by graphing \(y=|x| .\) Then use this graph to obtain the graph of \(y=|x-2|+1 . \quad \text { (Section } 1.6, \text { Example } 3)\)

This will help you prepare for the material covered in the first section of the next chapter. $$\text { Solve: } \frac{5 \pi}{4}=2 \pi x$$

Exercises \(153-155\) will help you prepare for the material covered in the next section. The formula \(A=10 e^{-0.003 t}\) models the population of Hungary, \(A\), in millions, \(t\) years after 2006 a. Find Hungary's population, in millions, for 2006,2007 \(2008,\) and \(2009 .\) Round to two decimal places. b. Is Hungary's population increasing or decreasing?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.