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 definition of a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, defined as f(x) = log_b(a) if and only if b^f(x) = a, where 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^k) = k * log_b(m).

Front

What is the value of log_3(81)?

Back

4, because 3^4 = 81.

Front

If log_7 + log(x^2 - 4) = log(35), what are the possible values of x?

Back

x = 3 or x = -3.

Front

Solve for x: log_10(x - 4) = 5.

Back

x = 100004.

Tags

CCSS.HSF.BF.B.5

Front

Solve the equation: log(2x) - log(5) = log(30).

Back

x = 75.