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Calculus I                                             Quiz #9                            April 20, 2004

Name____________________       R.  Hammack                          Score ____
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(1) Simplify the following expressions as much as possible.

(a)  FormBox[RowBox[{RowBox[{100, ^, RowBox[{(, RowBox[{-, 3.5}], )}]}], =}], TraditionalForm] FormBox[RowBox[{RowBox[{1, /, RowBox[{100, ^, 3.5}]}], =, RowBox[{1/100^(7/2), =, RowBox[{1/10 ... =, RowBox[{1/(10, 000, 000), =, StyleBox[1.*10^-7, FontWeight -> Bold]}]}]}]}]}], TraditionalForm]

(b) log_100(10) = 1/2

(c)  log_6(12) + log_6(3) = log_6(12 · 3) = log_6(36) = 2

(a)  log_3(3^15) =15

(b)  log(1000^(1/2)) =log_10(10^3^(1/2)) = log_10(10^(3/2)) =3/2


(2)  Write as a single logarithm:   log(x) + 2log(x^2 - 1) - log(x + 1) =
log(x) + log((x^2 - 1)^2) - log(x + 1) = log(x(x^2 - 1)^2) - log(x + 1) = log (x(x^2 - 1)^2/(x + 1))


(3)  Solve the equation:    2^(x - 4) = 3^(5x)

2^(x - 4) = 3^(5x)  log(2^(x - 4)) = log(3^(5x))  (x - 4) log(2) = 5x log(3) ... og(3)) x = log(2^4)/(log(2) - log(3^5)) = log(16)/(log(2) - log(243)) = log(16)/log(2/243)