1. ALGEBRA II HONORS @ THE NATURAL LOGARITHM

2. The natural logarithm, ln, is a logarithm! It acts, walks, and talks just like its cousin, log. The exception is that the natural log has only one base, e.This makes ln easier to use than regular logs.

3. Find to four decimal places: 1) ln6.3081.8418 What does this mean? e 1.8418 = 6.308 2) ln 0.01492-4.2051

4. Find : 3) lne 66 4) lne 0.083 0.083 5) e ln2011 2011 6) e ln0.1776 0.1776

5. 7) How does the natural logarithm, ln, and e compare? They are inverses. That is, they cancel each other. That is : lne x = e lnx = x

6. Let’s review the laws of logarithms :

7. 8) Tell whether the x-value is a solution of the equation. 8) Tell whether the x-value is a solution of the equation. lnx = -23; x = e -23 yes! Solve each equation. Round decimals to four places. 9) 2.5e -0.25x + 3.5 = 7-1.3459 485165195.4

8. 11) Roxanne inherited $1500 from her Aunt Caroline. Wisely, she deposited the money in Keen’s Great Bank. She made 3.75% interest compounded continuously. If Roxanne made no further deposits nor withdrawals, how much money will she have exactly 5 years after she deposited the money? Use That is, use the formula A = Pe rt where A = amount of money, P = principal, r = interest rate as a decimal, and t = time in years. $1809.35