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

Tags

CCSS.HSF.BF.B.5

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 product property of logarithms?

Back

The product property states that log_b(MN) = log_b(M) + log_b(N), where M and N are positive numbers.

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(M/N) = log_b(M) - log_b(N), where M and N are positive numbers.

Front

What is the power property of logarithms?

Back

The power property states that log_b(M^p) = p * log_b(M), where M is a positive number and p is any real number.

Front

Solve for x: 2(3)^(x+1) = 36

Back

x = 1.

Tags

CCSS.HSF.LE.A.4

Front

Write the expression as a single logarithm: log_5(3) + log_5(6) + log_5(9)

Back

log_5(162).

Front

Use multiple log properties to write as a single log: 3log_2(x) - log_2(y) + log_2(z)

Back

log_2(x^3 * z / y).

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.