Exponential and Logarithm 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.

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 is the natural logarithm?

Back

The natural logarithm is the logarithm to the base e, where e is approximately equal to 2.71828. It is denoted as ln(x).

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

How do you solve the equation log(x) + log(x) = log(25)?

Back

Combine the logs: log(x^2) = log(25). Then, set x^2 = 25, giving x = 5 or x = -5.

Front

What is the formula for continuous compound interest?

Back

The formula for continuous compound interest is A = Pe^(rt), where A is the amount, P is the principal, r is the rate, and t is time.

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

Evaluate log_2(8).

Back

log_2(8) = 3, because 2^3 = 8.

Front

What is the value of log_6(1/216)?

Back

log_6(1/216) = -3, because 6^(-3) = 1/216.