Logarithmic functions are complex and may create misconceptions. Students often see little, if any, reason for learning about them. Use the questions to guide an original response.

Give an example of an exponential equation whose solution is a negative number. How could you plot the graph of a logarithmic function without starting with the exponential graph?

Describe mathematical reasons and arguments that could convince a friend that log(M + N) ≠ logM + logN.

What misconceptions might these two problems present for students? Why is it important to address misconceptions early?

How would you respond to a student who sees little, or no, meaning in solving either problem?