In Chapter 4, we used logarithms to solve exponential equations. In this chapter, we consider logarithmic functions as models in their own right. We also study another base for exponential and logarithmic functions, the natural base $e\text{,}$ which is the most useful base for many scientific applications.
 Time elapsed Percent remembered $20$ minutes $58.2\%$ $1$ hour $44.2\%$ $9$ hours $35.8\%$ $1$ day $33.7\%$ $2$ days $27.8\%$ $6$ days $25.4\%$ $31$ days $21.1\%$