Define logarithm.
The power to which a base must be raised to produce a given number.
True or false: The logarithm of 1 is always 0.
TRUE
Fill in the blank: The base of a logarithm is the number raised to a power.
Exponent
What is the common logarithm?
A logarithm with base 10, often written as log(x).
What is the natural logarithm?
A logarithm with base e, often written as ln(x).
Define logarithmic scale.
A scale that uses logarithms to represent large ranges of values.
True or false: Logarithms can only be applied to positive numbers.
TRUE
What is the product rule for logarithms?
log_b(MN) = log_b(M) + log_b(N)
What is the quotient rule for logarithms?
log_b(M/N) = log_b(M) - log_b(N)
What is the power rule for logarithms?
log_b(M^p) = p * log_b(M)
Fill in the blank: The logarithm of a number less than 1 is ______.
Negative
What does log_b(b) equal?
1, because any base raised to the power of 1 is itself.
Define exponential function.
A function of the form f(x) = b^x, where b is a positive constant.
True or false: Logarithms and exponential functions are inverses.
TRUE
What is the change of base formula?
log_b(a) = log_k(a) / log_k(b) for any base k.
Fill in the blank: The inverse of log_b(x) is ______.
b^x
What is the logarithm of a product?
The sum of the logarithms of the factors.
What is the logarithm of a quotient?
The difference of the logarithms of the numerator and denominator.
Define logarithmic growth.
Growth that increases at a decreasing rate, represented by a logarithmic function.
True or false: Logarithmic functions are always increasing.
TRUE
What is the base of natural logarithm?
The constant e, approximately equal to 2.718.
Fill in the blank: The logarithm of 10 to the base 10 is ______.
1
What is the logarithm of 0?
Undefined, as no exponent can produce zero.
Define logarithmic equation.
An equation that involves a logarithm of a variable.
