1. Use the pattern you noticed about differences of logarithms with the same base to write a conjecture.

2. Assume the conjecture is true. Rewrite each expression as a single logarithm, then find its value.

3. If , , and , find the values of each logarithm. Explain or show your reasoning.

Let's work through some steps of a proof for your conjecture.

1. Rewrite both of these equations as logarithms, and circle your answers to use later.

2. Divide the left sides of the original equations, and set the quotient equal to the quotient of the right sides of the original equations.

3. Combine the exponents on the left side of the equation so that it is written with a single base.

4. Rewrite the last equation as a logarithm.

5. Use your circled equations to replace any and in that equation with equivalent logarithms.