Solve Exponential equations 1
Flashcard
•
Mathematics
•
11th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an exponential equation?
Back
An exponential equation is an equation in which a variable appears in the exponent. For example, in the equation 2^x = 8, x is the variable in the exponent.
2.
FLASHCARD QUESTION
Front
How do you solve the equation 8^(3x+3) = 8^6?
Back
Since the bases are the same, set the exponents equal: 3x + 3 = 6. Solving gives x = 1.
3.
FLASHCARD QUESTION
Front
What is the solution to the equation 3^3 = 3^(4x + 2)?
Back
Set the exponents equal: 3 = 4x + 2. Solving gives x = 1/4.
4.
FLASHCARD QUESTION
Front
How do you solve the equation 16^(x-3) = 8^(x-3)?
Back
Rewrite both sides with the same base: (2^4)^(x-3) = (2^3)^(x-3). This simplifies to 4(x-3) = 3(x-3). Since x-3 cannot be zero, solve for x = 3.
5.
FLASHCARD QUESTION
Front
What is the solution to the equation 8 = 2^(5x+7)?
Back
Rewrite 8 as 2^3: 2^3 = 2^(5x + 7). Set the exponents equal: 3 = 5x + 7. Solving gives x = -4/5.
6.
FLASHCARD QUESTION
Front
What is the base of an exponential function?
Back
The base of an exponential function is the constant that is raised to a variable exponent. For example, in the function f(x) = a^x, 'a' is the base.
7.
FLASHCARD QUESTION
Front
What is the general form of an exponential equation?
Back
The general form of an exponential equation is y = a * b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.
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