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ALGEBRA II HONORS @ THE NATURAL LOGARITHM
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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.
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Find to four decimal places: 1) ln6.3081.8418 What does this mean? e 1.8418 = 6.308 2) ln 0.01492-4.2051
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Find : 3) lne 66 4) lne 0.083 0.083 5) e ln2011 2011 6) e ln0.1776 0.1776
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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
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Let’s review the laws of logarithms :
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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
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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
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