Questions and Answers
The process of using each side of an equation as an exponent is also known as exponentiation.
True
If the base of the exponential expression equals the base of the log, the result is the ___?
Argument
All of the ___ properties of logarithms and exponents require that some corresponding part of the two sides are equal.
Equality
Each side of the equation must have only ___ term(s) before using the inverse properties.
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What is x in the equation 6^x = 1,296?
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What are the values of x in the equation e^x e^-3 = e^-2x2?
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What is the value of x in the equation e^x − 5 = 10?
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What is the result when solving log12 4x = log12 52?
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What is the value of x in the equation log3 (3x + 7) = log3 16?
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What is the value of x in the equation log2 (x − 1) = 3?
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Study Notes
Exponentiation and Logarithms
- Exponentiation involves using each side of an equation as an exponent.
- If bases of an exponential expression match the bases of a logarithm, the result is called the argument.
Properties of Logarithms
- All logarithmic and exponential properties rely on the necessity that corresponding parts of both sides are equal.
- Each side of the equation must contain only one term to effectively apply inverse properties.
Specific Equations and Solutions
- For the equation (6^x = 1,296), the solution is (x = 4).
- In the equation (e^x e^{-3} = e^{-2x2}), the solutions are (x = -\frac{3}{2}) and (x = 1).
- Solving (e^x - 5 = 10) yields (x = 7.303).
Logarithmic Equations
- The equation (\log_{12} 4x = \log_{12} 52) simplifies to find (x = 13).
- For (\log_{3} (3x + 7) = \log_{3} 16), the solution is (x = 3).
- The equation (\log_{2} (x - 1) = 3) results in (x = 9).
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Description
Test your knowledge with these flashcards from Abeka Algebra 2 Quiz 24. This quiz covers key concepts such as exponentiation, logarithms, and their properties. Sharpen your understanding of algebraic principles with these essential terms and definitions.
