Solving Logarithmic Equations
Flashcard
•
Mathematics
•
11th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a logarithm?
Back
A logarithm is the exponent to which a base must be raised to produce a given number. For example, log_b(a) = c means b^c = a.
2.
FLASHCARD QUESTION
Front
What is the change of base formula for logarithms?
Back
The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.
3.
FLASHCARD QUESTION
Front
What is the natural logarithm?
Back
The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.718.
4.
FLASHCARD QUESTION
Front
What is the product property of logarithms?
Back
The product property states that log_b(m * n) = log_b(m) + log_b(n).
5.
FLASHCARD QUESTION
Front
What is the quotient property of logarithms?
Back
The quotient property states that log_b(m / n) = log_b(m) - log_b(n).
6.
FLASHCARD QUESTION
Front
What is the power property of logarithms?
Back
The power property states that log_b(m^n) = n * log_b(m).
7.
FLASHCARD QUESTION
Front
How do you solve the equation 2log_5(7) = 3x + 1 log_5(49)?
Back
First, simplify log_5(49) to 2log_5(7). Then, set the equation to 0 to find x.
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