Natural Log and Power Rule of Log

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Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the definition of a logarithm?
Back
A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, if b^y = x, then log_b(x) = y.
2.
FLASHCARD QUESTION
Front
What is the natural logarithm?
Back
The natural logarithm is the logarithm to the base e, where e is approximately equal to 2.71828. It is denoted as ln(x).
3.
FLASHCARD QUESTION
Front
What is the Power Rule of Logarithms?
Back
The Power Rule states that log_b(a^c) = c * log_b(a). This allows you to bring the exponent in front of the logarithm.
4.
FLASHCARD QUESTION
Front
Convert the expression log_2(8) using the Power Rule.
Back
log_2(8) = log_2(2^3) = 3 * log_2(2) = 3.
5.
FLASHCARD QUESTION
Front
Write the equation 2^3 = 8 in logarithmic form.
Back
log_2(8) = 3.
6.
FLASHCARD QUESTION
Front
Write the equation ln(e^5) in logarithmic form.
Back
ln(e^5) = 5.
7.
FLASHCARD QUESTION
Front
What is the relationship between logarithmic and exponential forms?
Back
If log_b(x) = y, then it can be rewritten in exponential form as b^y = x.
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