© h.hofstede (h.hofstede@hogeland.nl)

       
1. a. 2x • 4  =  2/2x 
2x • 22 = 21 • 2-x
2x + 2 = 21 - x
x + 2 = 1 - x
2x  = -1
x = -1/2		  
       
  b. 3x • 34 = 1
3x + 4 = 30 
x + 4 = 0
x = -4		  
       
  c. 5x • 5-1 = 1/125
5x - 1 = 1/53
5x - 1 = 5-3
x - 1 = -3
x = -2		  
       
  d. 3/(32x + 1) = 27 
3 • 3-(2x + 1) = 33
31 - 2x - 1 = 33
-2x = 3
x = -11/2		  
       
  e. (2-2)-2 = 32 • 2x
2-2•-2 = 25 • 2x
24 = 25 + x
4 = 5 + x
x = -1 		 
       
  f. 16 • 4x = 64/42x
42 • 4x = 43 • 4-2x
42 + x =  43 - 2x
2 + x = 3 - 2x
3x = 1
x = 1/3		  
       
  g. 2³/2x = 16x
23 • 2-x = (24)x
23 - x  = 24x
3 - x = 4x
3 = 5x
x = 3/5		  
       
  h. 2x + 2x  = 218
2 • 2x = 218
21 + x = 218
1 + x = 18
x = 17		  
       
  i. 1 =  4/(2-x+ 3)
20 = 22 • 2-(-x + 3)
20 = 22 • 2x - 3
20 = 22 + x - 3
0 = 2 + x- 3
x = 1		  
       
  j. 32 • x5  = (x + 1)5
25 • x5 = (x + 1)5
(2x)5 = (x + 1)5
2x = x + 1
x = 1		  
       
2. a. x-3 • x4 = x-3 + 4 = x-1  
       
  b. x²/x-5  =  x2 • x - -5 = x2 + 5 = x7    
       
  c. 1/x5 • 1/x-3 =  x-5 • x - -3 = x-5 + 3 = x-2  
       
  d. x5 •  1/x8  = x5 • x-8 = x5 - 8 = x-3  
       
  e. x2 • 1/x  =  x2 • x-1  = x2 - 1 = x1 = x   
       
  f. x • x2 • x-6 = x1 • x2 • x -6  = x 1 + 2 - 6 = x-3  
       
  g.  x3 • (x6)-2 = x3 • x12 = x15  
       
  h. (x-2)4 • 1/x-2 = x-8• x - -2 = x-8 + 2 = x-6  
       
  i.  (x/x²)5 = (x • x-2 )5 = (x1-2)5 = (x-1)5 = x-1 • 5 = x-5   
       
3. a. 5p-2 • q3 = 5 • 1/p² • q3  = 5q³/p²  
       
  b. 1/8x-1 = 1/8 • 1/x = 1/(8x)  
       
  c. (2x)-3 • 1/x = 1/(2x)³ • 1/x  =  1/8x³ • 1/x = 1/(8x³•x) = 1/8x4  
       
  d. (2/3)-2 = 1/(2/3)² = 1/(4/9) = 9/4  
       
  e. (1/x-2 )5 = (x2 )5 = x10  
       
  f. 2/b-2 • (1/b)2 = 2•b2 • (b-1)2  = 2b2 • b-2  = 2b2 - 2 = 2b0 = 2 • 1 = 2  
       
4. R2 - S2 =  (3x + 3-x)2  - (3x - 3-x)
= (3x)2 + 2 • 3x • 3-x + (3-x)2 - (3x)2 + 2 • 3x • 3-x - (3-x)2
=  2 • 3x • 3-x  + 2 • 3x • 3-x
= 4 • 3x • 3-x
= 4 • 30
= 4
       
       

© h.hofstede (h.hofstede@hogeland.nl)