COLLEGE ALGEBRA   EXAM 4 HR1             NAME _____________________

SHOW ALL WORK ON THIS TEST OR ON SEPARATE PAPER.  Circle answers.

TURN IN ALL WORKSHEETS.  CALCULATORS ARE REQUIRED ON THIS TEST.

In 1 - 9, solve for the unknown: 

 1.    log ₅ 125 = x                          2.                                    3.  log ₅ 1 = x

 4.                                5.                                      6.  log ₅ x = − 1

  7.  log _b 16 = 2                               8.  log ₈  4  =  x                              9.  log _b  8  =  − 3

In 10 - 14,  simplify completely:

10.    =   ______                       11.    =  ______                      12.  =    ______

13.   =  ________              14.   =   _______                  15.   =   ______

In 16 - 21, use your calculator (round to nearest hundredth or give scientific notation):

16.   e ⁻⁷    = _______                    17.   ln 6  +  ln 100                            18.   ln (e⁵ + e⁷)

19.     6e²⁰ + 9e³⁰                       20.    log ₃   75                                  21.    –2 ln 8  +  6 ln 75

In 22 - 25,  solve for  x  (Give exact values--you may use “ROOT” to check!):

22.    27^{x + 4} = 9 ^{x −2}                                                  23.    12 ^x  = 7 ^{x + 4}

24.    log ₅ x = log₅ (x + 4) − 2                                  25.    log₂ x + log₂ (x +2) = 3

26.  The population of a rabbit farm is given by  y = 50 e^0.035t, where t is in years.

       a)  Estimate the population                     b)  How long will it take the population

             in 24 years.                                               to reach 1000?

27.       The population of a city in 1975 was 30,000.  In 1978, the population was 39,000. 

a)  Assuming that ,               b)  Use this value of k to predict the

      find the value of k.                           population of the city in 2005.

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COLLEGE ALGEBRA    EXAM 4    HR1 Solutions

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