Exponential and Logarithmic Functions

Front

What is the definition of 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 a positive real number, and x is the exponent.

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 given number. For example, in log_b(a) = c, b is the base.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If y = b^x, then x = log_b(y).

Front

What is the domain of the function f(x) = log_b(x)?

Back

The domain of f(x) = log_b(x) is x > 0.

Front

What is the range of the function f(x) = log_b(x)?

Back

The range of f(x) = log_b(x) is all real numbers.

Front

What does the logarithmic identity log_b(b) equal?

Back

log_b(b) = 1, because b raised to the power of 1 equals b.

Front

What is the value of log_5(25)?

Back

log_5(25) = 2, because 5^2 = 25.

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(M * N) = log_b(M) + log_b(N).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(M / N) = log_b(M) - log_b(N).

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(M^p) = p * log_b(M).