Exponential and Logarithmic Functions Exam

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 base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain another number. For example, in log_b(a) = c, b is the base.

Front

What is the inverse of an exponential function?

Back

The inverse of an exponential function is a logarithmic function.

Front

How do you solve the equation 5^x = 1?

Back

x = 0, because any number raised to the power of 0 equals 1.

Front

What is the transformation of the function f(x) = 2^x - 3?

Back

The function is shifted down 3 units.

Front

What is the horizontal asymptote of the function y = 2^x - 3?

Back

y = -3.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other.

Front

What is the natural logarithm?

Back

The natural logarithm is the logarithm to the base e, denoted as ln(x).

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

How do you express log(100) in terms of base 10?

Back

log(100) = 2, because 10^2 = 100.