3.4 - Solving Logarithmic Equations

Front

What is a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given 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 product rule of logarithms?

Back

The product rule states that log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(m / n) = log_b(m) - log_b(n).

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(m^n) = n * log_b(m).

Front

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

Back

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

Front

What is the definition of a logarithmic equation?

Back

A logarithmic equation is an equation that involves a logarithm of a variable or expression.

Front

How do you solve log(10x) + log(x - 3) = 2?

Back

Combine the logs: log(10x(x - 3)) = 2. Then, rewrite in exponential form: 10x(x - 3) = 100. Solve for x.

Front

What is the solution to log_x(1000) = 3?

Back

Rewrite in exponential form: x^3 = 1000. Therefore, x = 10.

Front

How do you solve -6log_3(x - 3) = -24?

Back

Divide by -6: log_3(x - 3) = 4. Rewrite in exponential form: x - 3 = 3^4. Therefore, x = 84.