What is the definition of a logarithm?
Evaluate Logarithms

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Mathematics
•
9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
A logarithm is the exponent to which a base must be raised to produce a given number. For example, if b^y = x, then log_b(x) = y.
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, where k is the new base.
3.
FLASHCARD QUESTION
Front
What is the value of log_b(1) for any base b?
Back
The value of log_b(1) is always 0, because any number raised to the power of 0 equals 1.
4.
FLASHCARD QUESTION
Front
What is the value of log_b(b)?
Back
The value of log_b(b) is always 1, because any number raised to the power of 1 equals itself.
5.
FLASHCARD QUESTION
Front
How do you evaluate log_b(1/x)?
Back
log_b(1/x) = -log_b(x), which means the logarithm of the reciprocal is the negative of the logarithm.
6.
FLASHCARD QUESTION
Front
What is the relationship between logarithms and exponents?
Back
Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.
7.
FLASHCARD QUESTION
Front
What is the value of log_2(128)?
Back
The value of log_2(128) is 7, because 2^7 = 128.
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