3.4 Solving Exp & Log Equations Mixed Practice #2

Front

What is the property of logarithms that allows you to combine logs with the same base?

Back

The property states that \( \log_b(m) + \log_b(n) = \log_b(m \cdot n) \).

Front

How do you convert a logarithmic equation to an exponential equation?

Back

If \( \log_b(a) = c \), then it can be rewritten as \( b^c = a \).

Front

What is the solution to the equation \( \log_2(x + 2) + \log_2(x) = 3 \)?

Back

The solution is \( x = 2 \).

Front

What is the solution to the equation \( \log_5(4x - 7) = \log_5(x + 5) \)?

Back

The solution is \( x = 4 \).

Front

What is the solution to the equation \( \log_2(x + 3) = 4 \)?

Back

The solution is \( x = 13 \).

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that \( \log_b(a) = \frac{\log_k(a)}{\log_k(b)} \) for any positive base \( k \).

Front

What is the definition of 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 solution to the equation \( \log_2(x^2 - 6) = \log_2(2x + 2) \)?

Back

The solution is \( x = 4 \).

Front

What is the quadratic equation derived from \( \log(5) = \log(x - 3) + \log(2x) \)?

Back

The quadratic equation is \( 0 = 2x^2 - 6x - 5 \).

Front

What is the product property of logarithms?

Back

The product property states that \( \log_b(mn) = \log_b(m) + \log_b(n) \).