/*! 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 59 Solve the logarithmic equation a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 59

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

Short Answer

Expert verified
The solution to the equation \(\log (3x+4)=\log (x-10)\) is \(x = -7\)

Step by step solution

01

Equate the arguments of the logarithms

From the properties of logarithms, if \(\log b = \log a\), then \(b = a\). Thus, set \(3x + 4 = x - 10\) to create an equation to solve.
02

Resolve into a linear equation

Solve the equation for x by subtracting x from both sides to get \(2x + 4 = -10\). Subtract 4 from both sides to result in \(2x = -14\).
03

Solve for x

To isolate x, divide both sides by 2. This yields \(x = -14 / 2\).
04

Calculate the value of x

Calculate the right-hand side to get the value of \(x = -7\).

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

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln x+\ln (x+1)=1$$

Find the domain, \(x\) -intercept, and vertical asymptote of the logarithmic function and sketch its graph. $f(x)=\log _{4} x$$

Solve the equation algebraically. Round your result to three decimal places. Verify your answer using a graphing utility. $$\frac{1+\ln x}{2}=0$$

Population The time \(t\) (in years) for the world population to double when it is increasing at a continuous rate of \(r\) is given by \(t=(\ln 2) / r\) (a) Complete the table and interpret your results. \begin{tabular}{|l|l|l|l|l|l|l|}\hline\(r\) & 0.005 & 0.010 & 0.015 & 0.020 & 0.025 & 0.030 \\\\\hline\(t\) & & & && &..\begin{array}{|l|l|l|l|l|l|l|} \hline r & 0.005 & 0.010 & 0.015 & 0.020 & 0.025 & 0.030 \\ \hline t & & & & & & \\ \hline \end{array}
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

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.