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Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. 4 - Exponential and Logarithmic FunctionsProblema 96
Capitolo 5, Problema 96

Solve each equation. 3|log x|−6=0

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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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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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Change of Base Property

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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Categorizing Linear Equations

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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Solving Linear Equations with Fractions
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