Exponential Equations

Flashcard
•
Mathematics
•
10th - 11th Grade
•
Hard
+1
Standards-aligned
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1.
FLASHCARD QUESTION
Front
Define an exponential equation.
Back
An exponential equation is an equation in which a variable appears in the exponent, typically in the form of a^x = b, where a is a positive constant, b is a positive number, and x is the variable.
2.
FLASHCARD QUESTION
Front
What is the base in an exponential equation?
Back
The base in an exponential equation is the constant 'a' in the expression a^x, which is raised to the power of the variable x.
3.
FLASHCARD QUESTION
Front
How do you solve the equation 5^(-3x - 1) = 25?
Back
Convert 25 to the same base: 25 = 5^2. Then, set the exponents equal: -3x - 1 = 2. Solve for x: x = -1.
4.
FLASHCARD QUESTION
Front
What is the solution to the equation 4^(p+2) = 64?
Back
Convert 64 to the same base: 64 = 4^3. Set the exponents equal: p + 2 = 3. Solve for p: p = 1.
5.
FLASHCARD QUESTION
Front
Solve for x: 2^x = 4^(x+1).
Back
Convert 4 to base 2: 4 = 2^2. Then, 4^(x+1) = (2^2)^(x+1) = 2^(2x + 2). Set the exponents equal: x = 2x + 2. Solve for x: x = -2.
6.
FLASHCARD QUESTION
Front
What is the value of a in the equation 5^(a + 2) = 1/125?
Back
Convert 1/125 to the same base: 1/125 = 5^(-3). Set the exponents equal: a + 2 = -3. Solve for a: a = -5.
7.
FLASHCARD QUESTION
Front
What is the property of exponents that allows you to set exponents equal when bases are the same?
Back
The property states that if a^m = a^n, then m = n, provided that a is not zero.
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