/*! 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 19 Solve the exponential equation a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 19

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$4\left(3^{x}\right)=20$$

Short Answer

Expert verified
The solution to the given exponential equation is approximately x = 1.465

Step by step solution

01

Isolate the exponential term

First, the exponential term \(3^{x}\) needs to be isolated. This can be done by dividing both sides of the equation by 4. This results in the new equation: \(3^{x} = \frac{20}{4}\)
02

Take the logarithm of both sides

In exponential equations, logarithms are often used to simplify the formula and solve for the variable. By taking the natural logarithm, denoted as \(ln\), of both sides of the equation, we get: \(ln(3^{x}) = ln(5)\). Using the power rule of logarithms, which states that \(ln(a^{b}) = b \cdot ln(a)\), the left side of the equation can be simplified to: \(x \cdot ln(3) = ln(5)\)
03

Solve for the variable

In the last step, solve for the variable \(x\) by dividing both sides of the equation by \(ln(3)\). To get \(x = \frac{ln(5)}{ln(3)}\). This can be computed just using a calculator.
04

Approximation

The exercise now asks to approximate this result to three decimal places. Using a calculator yields \(x \approx 1.465\). This is the required solution.

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

Data Analysis The table shows the time \(t\) (in seconds) required for a car to attain a speed of \(s\) miles per hour from a standing start. $$\begin{array}{|c|c|} \hline \text { Speed, S } & \text { Time, t } \\ \hline 30 & 3.4 \\ 40 & 5.0 \\ 50 & 7.0 \\ 60 & 9.3 \\ 70 & 12.0 \\ 80 & 15.8 \\ 90 & 20.0 \\ \hline \end{array}$$ Two models for these data are as follows. \(t_{1}=40.757+0.556 s-15.817 \ln s\) \(t_{2}=1.2259+0.0023 s^{2}\) (a) Use the regression feature of a graphing utility to find a linear model \(t_{3}\) and an exponential model \(t_{4}\) for the data. (b) Use the graphing utility to graph the data and each model in the same viewing window. (c) Create a table comparing the data with estimates obtained from each model. (d) Use the results of part (c) to find the sum of the absolute values of the differences between the data and the estimated values given by each model. Based on the four sums, which model do you think best fits the data? Explain.

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

Find the domain, \(x\) -intercept, and vertical asymptote of the logarithmic function and sketch its graph.\( \)y=\log \left(\frac{x}{7}\right)$$

In Exercises \(97-102,\) determine whether the statement is true or false given that \(f(x)=\ln x .\) Justify your answer. If \(f(x) < 0,\) then \(0 < x < 1\)

Use the acidity model given by \(\mathbf{p H}=-\log \left[\mathbf{H}^{+}\right],\) where acidity \((\mathbf{p H})\) is a measure of the hydrogen ion concentration \(\left[\mathbf{H}^{+}\right]\) (measured in moles of hydrogen per liter) of a solution. Apple juice has a pH of 2.9 and drinking water has a pH of \(8.0 .\) The hydrogen ion concentration of the apple juice is how many times the concentration of drinking water?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

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.