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 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.

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).

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, typically represented by the function f(t) = a * e^(-kt), where 'k' is a positive constant.

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.

Front

What is the value of log_10(100)?

Back

log_10(100) = 2, because 10^2 = 100.

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(x^k) = k * log_b(x).

Front

Solve for x: 2^x = 16.

Back

x = 4, because 2^4 = 16.