/*! 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 50 Solve the logarithmic equation a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 50

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln \sqrt{x-8}=5$$

Short Answer

Expert verified
The approximate answer to three decimal places is \( x = 22026.466 \)

Step by step solution

01

Understanding the Equation

The given equation is \( \ln \sqrt{x-8} = 5 \). Here, 'ln' stands for a natural logarithm, which is a logarithm to the base 'e', where e is an irrational and transcendental number approximately equal to 2.718281. We are required to solve this equation for 'x'.
02

Convert Logarithm to Exponential

To remove the natural logarithm, we can write it as an exponential equation. The base for 'ln' is 'e'. So now this equation can be written as \( e^5 = \sqrt{x-8} \).
03

Square Both Sides

To remove the square root, square both sides will isolate x. By squaring both sides of the equation we get, \( (e^5)^2 = (\sqrt{x-8})^2 \) which further simplifies to \( e^{10} = x-8 \).
04

Solve for x

Add 8 to both sides of the equation to isolate x, you will get \( x = e^{10} + 8 \).

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

Function \(\quad\) Value $$ g(x)=-\ln x \quad x=\frac{1}{2}$$

The graph of \(f(x)=\log _{3} x\) contains the point \((27,3)\)

True or False? In Exercises 83 and \(84,\) determine whether the statement is true or false. Justify your answer. The graph of \(f(x)=\log _{6} x\) is a reflection of the graph of \(g(x)=6^{x}\) in the \(x\) -axis.

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log _{2} x+\log _{2}(x+2)=\log _{2}(x+6)$$

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

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Mechanics 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.