RADICALS 4

EXPONENTIALS 4

Find x if 64^x = 0.125; find x.

Solution

64^x = 0.125

(2⁶)^x = 0.125          [since 64=2⁶ ]

2^6x = 0.125          

2^6x = ¹²⁵/₁₀₀₀     [converting 0.125 into fraction]       

2^6x = ¹/₈    [after simplifying]       

2^6x = 8^-1           [since ¹/_a=a^-1]

2^6x = (2³)^-1

2^6x = 2^{3 x-1}           

2^6x = 2^-3           [since (a^c)^d =a^cd]

2^6x = 2^-3           [same bases cancel out]

6x = -3         

6x = -3 ^-1        

6      6 ₂

x= ^-1/2

Hence x= ^-1/2  .

TRY THIS…………………….

Find x if 16^2m = 0. 5; find m.

LOGARITHMS 5

FUNCTIONS 1

If f(x) = |x - 24| evaluate f(-50)

solution

f(x) = |x - 24|

f(-50) = |-50- 24|

f(-50) = |-74| = 74 since any number out of absolute signs is +ve.

Hence f(-50) = 74

TRY THIS..................

If f(x) = |x - 30| evaluate f(-15)

RADICALS 3

ALGEBRA 1

If  x+4y = 1            find  ^x/y             

    x-3y     4

solution

x+4y = 1           

x-3y     4

1(x-3y) = 4(x+4y)           [after cross multiplying]

x-3y = 4x+16y

x - 4x = 16y + 3y

-3x = 19y

¹-3x =   19y         [dividing by -3 both sides]

₁-3        -3

x =   19y         

        -3

      

x =     19y ¹   [dividing by y both sides]    

y       -3y ₁

x = ^-19/₃

y    

Hence ^x/_y = ^-19/₃answer.          

TRY THIS......................

If  x+2y = 1            find  ^x/y             

    x- 2y     6

NUMBER LINE 1

AXIS OF SYMMETRY 1

Find the axis of symmetry for F(x) = 6x² + 48x + 8

Solution

a=6, b=48

Axis of symmetry = -b/2a

                                  =  -(48)

                                       2 x 6

                                 =    -48

                                         12

                                 =   -4

                                       

Hence the axis of symmetry is ^-10/3

TRY THIS...............

Find the axis of symmetry for F(x) = 5x² + 40x - 2

MATRIX 3

LOGARITHMS 4

Evaluate Log₂(256 x 64 x 32).

Solution

= Log₂(256 x 64 x 32)

= Log₂256 +  Log₂64 +  Log₂32                   (applying the product rule)

= Log₂2⁸ +  Log₂2⁶    +  Log₂2⁵                      ( 256= 2⁸ and 64=2⁶ ,32=2⁵)

= 8Log₂2 +  6Log₂2    +  5Log₂2         ( remember  Log_aa^c = cLog_aa )

= (8 x 1) +  (6 x 1) +  (5 x 1)                  ( remember  Log_aa = 1 )

= 8 + 6 + 5

= 19

hence Log₂(256 x 64 x 32) = 19

TRY THIS...............

Evaluate Log₂(512 x 128 x 32).