## Indices Questions

1.  Evaluate the value of x in

81 + 3 = 246.

2.  Solve for y in the equation:-

5(2y+1) = 4(5)y+1 – 15

3.  Without logarithm tables or calculators, evaluate: 25¾ x 0.92 x 22 in the form A/B

where A and B are integers 5 x 33

4.  Find the value of x given that :

2ˣ=0.0625 (x is an integer)

6. Find the value of x which satisfies the equation 16x2 = 8 4x – 3

7.  Solve the equation;

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9 x+1 + 3 2x + 1= 36

8.  By letting P = 4-y in the equation:

4-2y
+1 – 3 x 4-y – 10 = 0

(a) Write the above equation in terms of P

(b) Hence find the possible values of y

9.  Solve for x in the equation.

10.  In the expansion of ax – 2
the constant term is 4860. Find the value of a.

x2

1.  34 x 34x + 34x = 246

34x (81 + 1 ) = 246

82 x 34x = 246

82 82

34x = 31

4x = 1

x = 1

4

2.  52y x51 = 4(5y+1) – 15

5y x 5y x 51 = 4 x 5y x 51 – 15

Let 5y = t

5t2 = 20t – 15

t2 = 20t – 15

t2 – 4t + 3 = 0

(t-1) (t-3) = 0

t = 1 or 3

5y = 1= 5o

Or 5y = 3 y = log 3

log 5 = 0.6826

3.  CBD = 90 – 42 = 48o

Angle of triangle add to 180o

DOB = 180o – 42 = 138o

DAB = 138o = 69o

2

Angle at circumference is half the nagle substended at centre by same chord

CDA

ABD= 90 – 48 = 42o

180-111=69o

CDA = 90 + 69o = 159o

DAB = 69o

DAB = 69o

ABD = 42o

So two angles are equal hence it is asoccesters

4.  25 ¾ = ( 25 ½ ) 3/2 = 5

0.92 = ( 9/10)2 = 92/100

22 = 22

(√5)3 x 92 x 22

(√5)5 x 102 x 33

3 x 4

(√5)2 x 102

3 = 3

5 x 25 125

5.  2x = 0.0625 = 625

1000

2x = 1 = 2-4

16

x = -4

6.  16x2 = 8 4x-3

24×2 = 2 3(4x -3)

= 4x2 = 12 x -9

= 4x2 – 12x + 9 = 0

(2x-3)2 = 0

2x-3 = 0

x = 1.5

 No5.627(0.234)3    8.237 2.399 x 10-3 Log0.7503 T. 3692 x 32.8579 0.4779 0.9158 23.3800  = 0.002399

7.  9 x+ 1 + 32x + 1 = 36

32x + 2 + 32x + 1 = 36

32x (9 + 3) = 36

32x = 31

2x = 1

x = ½

8.  (a) 4p2 – 3P – 10 =0

(b) 4p2 – 8p + 5p =0

(4p +5) (p-2) = 0

p1 = -5/4, p =2

When y = -5/4,

4-y = -5

4

y = log 4 (-5)

2

P = 2

4-y = 2

2-2y = 21

y = -1/2

9.

1 = 1

16x 32

1 = 1

24x 25

2 + x = 2

-4x2 + x + 5 = 0

4x2 – x – 5 = 0

4x2 – 5x + 4x – 5 = 0

x(4x – 5) + 1(4x – 5) = 0

x = -1 or x = 5

4

10.  15 (ax)4 (-2/x2) = 4860

60a4 = 4860

a4 = 81

a = 3

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