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Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 4 - Exponential and Logarithmic FunctionsProblem 96
Chapter 5, Problem 96

Solve each equation. 3|log x|−6=0

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1
Start with the given equation: \(3|\log x| - 6 = 0\).
Isolate the absolute value expression by adding 6 to both sides: \(3|\log x| = 6\).
Divide both sides by 3 to solve for the absolute value: \(|\log x| = 2\).
Recall that \(|A| = B\) means \(A = B\) or \(A = -B\). So, set up two equations: \(\log x = 2\) and \(\log x = -2\).
Solve each equation for \(x\) by rewriting in exponential form: \(x = 10^2\) and \(x = 10^{-2}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Properties of Logarithms

Logarithms are the inverse operations of exponentiation. Understanding how to manipulate log expressions, such as log x, is essential. The domain of log x requires x to be positive, which affects the solution set of equations involving logarithms.
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Absolute Value Equations

An absolute value equation like |log x| = k splits into two cases: log x = k and log x = -k. Solving both cases is necessary to find all possible solutions. Recognizing this helps in correctly handling equations involving absolute values.
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Solving Linear Equations

After isolating the absolute value expression, solving the resulting linear equation involves basic algebraic steps. This includes adding, subtracting, multiplying, or dividing both sides to isolate the variable or expression, preparing it for further solving.
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Related Practice
Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. ln x + ln(2x) = ln(3x)

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Textbook Question

Solve each equation. 2|ln x|−6=0

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Textbook Question

Solve each equation. 3x2=453^{x^2} = 45

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. ln(5x) + ln 1 = ln(5x)

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Textbook Question

Find all zeros of f(x) = x³ + 5x² – 8x + 2.

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Textbook Question

Determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. log(x + 3) - log(2x) = [log(x + 3)/log(2x)]

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