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MATH 154 PRACTICE MIDTERM II

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Do all your work and give all your answers on you own sheet of paper.  Show your work.

Printable Key

Problem 1 

Solve the following:

A.     (10 Points)   log₆(x - 5) + log₆(x)  =  2  

Solution   

B.  (10 Points)  2^2x-1  =  5^3x-2  

Solution  

C.  (10 Points)   Use a calculator to evaluate  log₇ 51

  Solution

Problem 2 

The clarity C (in feet) of Lake Tahoe t  years since 1990 can be modeled by the equation

        C(t)  =  45e^-t/25

A.     (9 Points)   How clear was the lake in 1995.

Solution

B.     (10 Points)   When will the clarity of the lake only be 5 feet?

  Solution

Problem 3   

One muffin, two pies, and three cakes cost $23.  One Muffin, three pies , and two cakes cost $21.  One muffin, four pies, and five cakes cost $39.  Find the cost of each.

Solution

Problem 4   (10 Points)  

 Solution

Problem 5  (20 Points)    Sketch the graph of the following function:

        y  =  2^x - 3

Solution

Problem 6  Expand each logarithm.  Simplify where possible.  Assume all variables are such that all expressions are defined.

A.     (10 Points)                 x⁵y²
                        log₃                
                                   81

Solution              

B.     (10 Points)         

Solution

Problem 7 Answer the following True or False.  If True, explain your reasoning, if False, explain your reasoning or show a counter-example.

A.     (7 Points)   The domain of the function  y  =  log_b x  is (0,  )  for all b > 0.

Solution

B.     (7 Points)   If a linear system of three equations with three unknowns has (1,2,3) as a solution then (4,5,6) cannot also be a solution

Solution

C.     (7 Points)  If the vertex of a parabola has y-coordinate 3 and the directrix is y = 2, then the parabola has no x-intercepts.

Solution

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