/*! 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 22 Solve the exponential equation a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 22

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$6^{x}+10=47$$

Short Answer

Expert verified
The approximate solution to the equation is \(x = 2.279\)

Step by step solution

01

Isolate the Exponential Term

Start by subtracting 10 from both sides of the equation. This gives us the equation \(6^{x}=37\)
02

Apply Natural Logarithm

Next, apply the natural logarithm to both sides of the equation to get rid of the base 6. This gives us the equation \(\ln(6^{x}) =\ln(37)\)
03

Simplify Left Hand Side

By properties of logarithms, on the left side we can bring the exponent (x) down as a coefficient to give: \(x \cdot \ln(6) = \ln(37)\)
04

Isolate x

Now, divide both sides of the equation by \(\ln(6)\) to isolate x. This gives us \(x = \frac{\ln(37)}{\ln(6)}\)
05

Use a Calculator to Calculate the Value of x

Use a calculator to find the numerical value of x, approximated to three decimal places.
06

Solve for x

Given \(x = \frac{\ln(37)}{\ln(6)}\), calculate the result to three decimal digits. Make sure the calculator mode is in natural logarithm mode, not common logarithms (log base 10)

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 the functions \(y_{1}=\ln x-\ln (x-3)\) and \(y_{2}=\ln \frac{x}{x-3}\) in the same viewing window. Does the graphing utility show the functions with the same domain? If so, should it? Explain your reasoning.

Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$10-4 \ln (x-2)=0$$

Using the One-to-One Property In Exercises \(73-76,\) use the One-to-One Property to solve the equation for \(x\). $$\ln (x+4)=\ln 12$

Write the logarithmic equation in exponential form. $$\ln 7=1.945 \ldots$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log (3 x+4)=\log (x-10)$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.