Exponential and Logarithmic Functions

Front

What is 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 difference between exponential growth and decay?

Back

Exponential growth occurs when the base of the exponent is greater than 1 (b > 1), while exponential decay occurs when the base is between 0 and 1 (0 < b < 1).

Front

What is the logarithm of a number?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to produce a given number.

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 certain value. For example, in log_b(a) = c, b is the base.

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.

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^n) = n * log_b(m).

Front

Evaluate log_10(100)

Back

2, because 10^2 = 100.

Front

Evaluate log_2(8)

Back

3, because 2^3 = 8.