1. Use the pattern you noticed about logarithms of expressions with an exponent to write a conjecture.

2. Assume the conjecture is true. Rewrite each expression using your conjecture, then find the value of the expression.

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 the equation as a logarithm, and circle your answer to use later.

2. Raise each side of the original equation to the power of .

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

4. Rewrite the last equation as a logarithm with a base of .

5. Use your circled equation to replace any in that equation with an equivalent logarithm.