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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   Sketch the graphs of the given functions:

A.      (10 Points)      x²
                               + 4y² = 1
                        9            

Solution

B.   (10 Points)   x² + y² + 2x - 4y - 4  =  0    

Solution

C.   (10 Points)  

Solution

Problem 4   (10 Points)   Find the equation of conic with the graph shown below:

  Solution

Problem 5  (20 Points)    Determine whether the function is 1-1. If it is find the inverse and graph both functions on the same set of axes.

A.  f(x)  = (1/2)^x

Solution

B.  f(x)  =  |x - 4|

  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)   The equation    is undefined since you cannot take the square root of a negative number.

Solution

C.     (7 Points)   If f(x)  = x³ + x   then  f ^-1(3)  =  1 .

Solution

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