Logarithmic Properties

Multiple Choice

Which of the following best describes a logarithm?

• A mathematical operation that finds the exponent needed to produce a given number from a specific base

• A function that always increases

• A type of geometric sequence

• A method for solving linear equations

Open Ended

Why is it important to understand the relationship between exponential and logarithmic functions in real-life situations?

Open Ended

Explain how an exponential equation can be rewritten in logarithmic form, using the example 2^3 = 8.

Multiple Choice

Which property of logarithms allows you to combine $$\log_4(16)+\log_4(4)$$ into a single logarithm?

• Sum (Product) Rule

• Difference (Quotient) Rule

• Power Rule

• Reciprocal Rule

Property 2: Difference (Quotient) Rule

Multiple Choice

If $$\log_5(125)-\log_5(25)=\log_5(125\div25)$$ , what is the value of log_5(125 ÷ 25)?

• $$\log_5(5)$$

• $$\log_5(125)$$

• $$\log_5(625)$$

• $$\log_5\left(3125\right)$$

Multiple Select

Which of the following are correct applications of the Power Rule for logarithms?

• $$\log_2(3^4)=4\log_2(3)$$

• $$\log_2(5^3)=3\log_2(5)$$

• $$\log_2(2^6)=6\log_2(2)$$

• $$\log_2(4^2)=2\log_2(8)$$

Multiple Choice

Which of the following correctly represents the change of base rule for logarithms?

• $$\log_a(b)=\log b/\log a$$

• $$\log_a(b)=\log a/\log b$$

• $$\log_a(b)=\log b*\log a$$

• $$\log_a(b)=\log b+\log a$$

Open Ended

Explain how the inverse rule for logarithms (Property 7) relates to the change of base rule (Property 6). Provide an example to illustrate your explanation.

Multiple Select

Which of the following is a learning target for this lesson on exponential and logarithmic functions?

• I can understand the relationship between exponential functions and logarithmic functions.

• I can solve quadratic equations by factoring.

• I can use the definition concept of logarithm to determine an output.

• I can graph linear equations.

Open Ended

How do exponential functions and logarithmic functions relate to each other in real-life phenomena?