Exponential and Logarithmic Equations

Flashcard
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the definition of 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 definition of a logarithmic equation?
Back
A logarithmic equation is an equation that involves a logarithm of a variable, typically in the form of log_a(x) = b, where a is the base, x is the argument, and b is the result.
3.
FLASHCARD QUESTION
Front
What is the relationship between exponential and logarithmic functions?
Back
Exponential and logarithmic functions are inverses of each other. If y = a^x, then x = log_a(y).
Tags
CCSS.HSF.BF.B.5
4.
FLASHCARD QUESTION
Front
How do you solve an exponential equation of the form e^(kx) = C?
Back
To solve e^(kx) = C, take the natural logarithm of both sides: kx = ln(C), then solve for x: x = ln(C)/k.
5.
FLASHCARD QUESTION
Front
What is the change of base formula for logarithms?
Back
The change of base formula states that log_a(b) = log_c(b) / log_c(a) for any positive c.
6.
FLASHCARD QUESTION
Front
What is the product property of logarithms?
Back
The product property states that log_a(xy) = log_a(x) + log_a(y).
7.
FLASHCARD QUESTION
Front
What is the quotient property of logarithms?
Back
The quotient property states that log_a(x/y) = log_a(x) - log_a(y).
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