Solving Exponentials Using Logarithms

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•
Mathematics
•
9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an exponential function?
Back
An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.
2.
FLASHCARD QUESTION
Front
What is a logarithm?
Back
A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number. For example, if b^y = x, then log_b(x) = y.
3.
FLASHCARD QUESTION
Front
How do you convert an exponential equation to a logarithmic form?
Back
To convert an exponential equation a^b = c to logarithmic form, you write it as log_a(c) = b.
4.
FLASHCARD QUESTION
Front
What is the base of a logarithm?
Back
The base of a logarithm is the number that is raised to a power to obtain a certain value. For example, in log_2(8) = 3, the base is 2.
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
How do you solve an exponential equation using logarithms?
Back
To solve an exponential equation, take the logarithm of both sides, then use properties of logarithms to isolate the variable.
7.
FLASHCARD QUESTION
Front
What is the property of logarithms that states log_a(m * n) = ?
Back
log_a(m) + log_a(n) (the product property of logarithms).
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