Log Eq and Word Problems

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number. For example, log_b(a) = c means b^c = 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 relationship between exponential and logarithmic functions?

Back

Exponential functions can be expressed as logarithmic functions and vice versa. If y = b^x, then x = log_b(y).

Front

How do you solve an equation of the form log_b(x) = c?

Back

To solve log_b(x) = c, rewrite it in exponential form: x = b^c.

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

How do you express 2^x = 32 in logarithmic form?

Back

The logarithmic form is x = log_2(32).

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is P(t) = P_0 * e^(rt), where P_0 is the initial amount, r is the growth rate, and t is time.

Front

How do you find the time it takes for a population to reach a certain size using exponential growth?

Back

Set the exponential growth equation equal to the target population and solve for t.