Domanda del libro di testo
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb x3
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Ch. 4 - Exponential and Logarithmic Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 5, Problema 15
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 6(x−3)/4=√6
Guida verificata passo dopo passo1
Recognize that the equation is \(6^{\frac{x-3}{4}} = \sqrt{6}\). The goal is to express both sides as powers of the same base.
Rewrite the right side, \(\sqrt{6}\), as a power of 6. Recall that \(\sqrt{6} = 6^{\frac{1}{2}}\).
Now the equation becomes \(6^{\frac{x-3}{4}} = 6^{\frac{1}{2}}\).
Since the bases are the same and the equation is an equality, set the exponents equal to each other: \(\frac{x-3}{4} = \frac{1}{2}\).
Solve the resulting linear equation for \(x\) by multiplying both sides by 4 and then isolating \(x\).
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Exponential Equations
Exponential equations involve variables in the exponent position. Solving these requires understanding how to manipulate and isolate the variable in the exponent to find its value.
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Solving Exponential Equations Using Logs
Expressing Numbers as Powers of the Same Base
To solve exponential equations, rewrite both sides with the same base if possible. This allows you to set the exponents equal to each other, simplifying the equation to a solvable form.
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Properties of Exponents
Properties such as the power of a power and the product of powers help simplify expressions. For example, the square root of a number can be written as that number raised to the 1/2 power, aiding in rewriting terms with common bases.
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04:06Rational Exponents
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