Exponential and Logarithmic Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where a is a constant, b is the base (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.

Tags

CCSS.HSF.BF.B.5

Front

How do you convert a logarithmic equation to exponential form?

Back

To convert log_b(a) = c to exponential form, rewrite it as b^c = a.

Tags

CCSS.HSF.BF.B.5

Front

What is the product rule of logarithms?

Back

The product rule states that log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(m / n) = log_b(m) - log_b(n).

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(m^n) = n * log_b(m).

Front

What is the value of log_5(25)?

Back

The value of log_5(25) is 2, because 5^2 = 25.

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 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).

Tags

CCSS.HSF.BF.B.5

Front

What is the value of log_2(8)?

Back

The value of log_2(8) is 3, because 2^3 = 8.

Tags

CCSS.HSF.BF.B.5