HPC Unit 6: Exponential and Logarithmic Equations

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, in the equation 2^x = 8, x is the variable in the exponent.

Front

What is a logarithmic equation?

Back

A logarithmic equation is an equation that involves a logarithm of a variable. For example, log_b(x) = y means that b^y = x.

Front

What is the half-life of a substance?

Back

The half-life of a substance is the time required for half of the substance to decay or be removed. It is commonly used in nuclear physics and chemistry.

Front

How do you solve an exponential equation?

Back

To solve an exponential equation, you can take the logarithm of both sides or rewrite the equation in a form that allows you to isolate the variable.

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

How do you evaluate log_b(a)?

Back

To evaluate log_b(a), you need to find the exponent x such that b^x = a.

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 value of log_5(25)?

Back

log_5(25) = 2, because 5^2 = 25.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is N(t) = N_0 * e^(-kt), where N_0 is the initial amount, k is the decay constant, and t is time.

Front

How do you find the half-life using the decay formula?

Back

To find the half-life (t_1/2), use the formula t_1/2 = ln(2) / k, where k is the decay constant.