IB Math SL1/Intens Precalc - Chapter 4 Review 
           
          No Calculator 
          1.     a)  Show that xlogby can be written as  ylogbx .    [Hint: how can you rewrite x using log ?] 
                                                                                                     b
                 b)  Hence, or otherwise, evaluate 4log27. 
           
          2.  Solve for x: 
                 a)  log (x2) =(log x)2                   b)  log (x2 −6)= 2 
                       2           2                             4
                                                                 x
                 c)  e2x = 5ex −2                         d)   2x+1 ln3=ln16 
                                                             (      )
           
                 e)  3x+1 = 4x−2                          f)  log x = log (4x+4) 
                                                                4      16
           
                 g)  log2(2x+1)−log4 x =log23 
           
           
          With Calculator 
          1.  If log 4 2 = x,log y = 4, and y = 4x2 −2x−6+ z, find y. 
                  2            z
           
          2.  Find the exact value of the product of the solutions to the equation 8e2 −2eln x =(ln x)2. 
           
          3.  The solution of 22x+3 = 2x+1 +3 can be expressed in the form a+log b where a,b∈
. Find 
                                                                                2
             the values of a and b. 
           
          The following two questions came from 2011 IB tests. 
          4.  Let  f (x) = 3ln x and g(x) = ln5x3 
                 a)  Express g(x) in the form  f (x)+lna where a∈
+. 
                 b)  The graph of g is a transformation of the graph of f. Give a full geometric description 
                    of this transformation. 
           
          5.  Let  f (x) = log x +log 16−log 4 for x > 0. 
                           3 2     3       3
                 a)  Show that  f (x) = log3 2x. 
                 b)  Find the value of  f (0.5) and of f (4.5). 
             The function f can also be written in the form  f (x) = lnax . 
                                                                   lnb
                 c)  i)  Write down the values of a and of b. 
                      ii)  Hence on graph paper, sketch the graph of f , for −5≤ x ≤5,−5≤ y ≤5. 
                      iii) Write down the equation of the asymptote. 
                 d)  Write down the value of  f −1(0). 
             The point A lies on the graph of f. At A, x = 4.5. 
                 e)  On your diagram, sketch the graph of  f −1, noting clearly the image of point A. 
             ANSWER KEY 
              
             No Calculator 
             1.       a)  Hint:   x = blogbx                                b)  49 
             2.       a)  1,4                                               b)    8 
                                                                                 ln
16
                             
5+ 17          
5− 17                               3        log 16−1
                      c)  ln           ,ln                              d)           or      3        or 0.762 
                                  2             2                              ln9              2
                                                      
                      e)   log48  or log ( 1 ) or 13.457                    f)  2+2 2  
                               
 4          3  48
                           log             4
                                3
                      g)   1 ,1 
                           4
              
              
             Calculator 
             1.   y =16 
             2.   x = e−2e 
             3.  a = −2,b =3 
             4.       a)   f (x)+ln5                               b)  vertical translation up ln5 units 
             5.       a)  Yes, it does. 
                      b)   f (0.5) = 0       f (4.5) = 2  
                      c)  i) a = 2,b = 3                  ii)  see below                     iii)   x = 0  
                      d)   1  
                           2
              
                      e)