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Unformatted text preview: MAP 103: Proﬁciency Algebra Homework #14
DUE: TUESDAY, DEC. 8, 2009 1. Apply the rules for logarithms to write the following expressions in simplest form. (a) log(x4 y 2 z 3 ) 64 4 100x y (b) log 10z 3 2. Apply the rules for logarithms to ﬁnd the value of the following expressions. 1 (a) log5 25 (b) log8 2 (c) log 1000 √ (d) log 7 7 3. Apply the rules for logarithms to ﬁnd the value of the following expressions. (a) 2log4 64 √ (b) 3 log2 16 √ (c) log2 1 + log3 27 + log4 64 + log5 25 + log8 88 + log5 5 4. Rewrite as a function of x the following expressions. (a) log2 y = 4 + 3 log2 (3x) 1 (b) 4 ln y = 2 + 2 ln(4x) 5. Solve for x in the following exponential equations. Check the solution. (a) 92x+1 = 273x−2 (b) 2x+2 = 41−x 2 (c) 27x +1 = 243 6. Apply rules for logarithms as a guide and solve the exponential equations for x. Check the solution. (a) 3x = 5 (b) 2√ x = 4 e2 (c) ( 2)x = 10 (d) e2x − 5ex + 6 = 0 7. Find in exact value the logarithmic expression: √ 4 9log2 4 . 8. Find the equation for an exponential function f (x) = abx satisfying that f (0) = 2 and f (3) = 16. 9. Solve for the unknown x each of the logarithmic equations. Be sure to check that your solution is a member of the domain for the given logarithms. (a) log2 x + log2 x3 = 3 (b) log4 (x + 2) + log4 (x + 3) = 2 10. After 10 years a given amount of element M will have decayed to half of its original amount. What is the decay rate k in the decay model A = A0 ekt ? Here A is the amount of M after decay, A0 is the amount of M before decay, e is a number, t is the amount of time and k is the decay rate. ...
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This note was uploaded on 04/18/2010 for the course MAP 103 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.
- Fall '08