# Essay on UNIT 1 Key Questions 1 2 3 4 5

1.

a) (2x3)(-7x5)= -14x8

b) -45x5y7z9/9x7y7z5= -5z4/x2

c) (-5x4)3= (-53)(x12)= -125x12

d) (3x4y5z7)5/(-3x3yz4)7=243y18z7/-2187x= y18z7/-9x

e) (xa+b)a-b/(xa-2b)a+2b= (xa^2-b^2)/(xa^2-4b^2)= x3b^2

2.

a)6-2= 1/62=1/36

b)253/2=(2√25)3=53=125

c) -85/3=(3√-8)5= (-2)5= -32

d) 625(-3/4)=1/(4√625)3=1/53= 1/125

3.

a) 93x272x813= (32)3x(33)2x(34)3= 36x36x312= 324

b) 57x253/1254= (57x(52)3)/(53)4= 57x56/512=513/512= 5

4.

5. To find the equation of the exponential function that pass through (0,-1),(-1,-3),(-2,-9) with x-axis as asymptote:

Formula: y=a(bx) y-intercept (0,-1)

1) Point 1 (-1,-3) 2) Point 2 (-2,-9)

(-3)=ab-1 (-9)=ab-2

-3/b-1=a (-9)/b-2=a

Find b-

Since a=a

Therefore -3/b-1=

*…show more content…*

4x=7+3

4x=10 x=10/4 x=5/2

b)

15x2+x-6=0

15x2-9x+10x-6=0

3x(5x-3)+2(5x-3)=0

(3x+2)(5x-3)=0

3x+2=0 or 5x-3=0

3x=-2 or 5x=3 x= -2/3 or x=3/5

c)

3x2-8x-1=0

x=(-(-8)±(√(-8)2-4(3)(-1)))/(2(3)) x=(8±√76)/6 x=(4+2√19)/3 or x=(4-2√19)/3

25.

a)

34x-5= 1/27

34x-5=3-3

4x-5=-3

4x=-3+5

4x=2 x=1/2 b)

4x-2=8x+1

(22)x-2=(23)x+1

2x-4=3x+3

2x-3x=3+4

-x=7

x=-7

26.

a)

2x+3-2x=224

2x(23-1)=224

2x(8-1)=224

2x(7)=224

2x=32 x=5 b)

4(22x)-31(2x)-8=0

4((2x)2)-31(2x)-8=0 sub z as 2x

4(z2)+31z-8=0

4z2+32z-z-8=0

4z(z+8)-(z+8)=0

(4z-1)(z+8)=0

4z-1=0 or z+8=0 z=1/4 or z=-8 sub 2x back in

2x=1/4 or 2x=-8 x= -2 since 2x=-8 does not give a real number

27. Solve the following systems

2x+3y=128, 23x-y=2 x+3y=7, 3x-y=1 x=7-3y 3(7-3y)-y=1

21-9y-y=1

21-10y=1

-10y=-20

y=2 sub y=2 into x=7-3y x=7-(3(2)) x=1

The answer is x=1, y=2

28. Solve 3x=72 using interpolation and logarithm

Interpolation:

Since 72=49, 33=27, 34=81

49 is between these numbers

Since 3x=49, x is between 3 and 4

49-27=22, 81-27=54

This means that of the 54 numbers from 27 to 81, 49 is the 22nd

So 49 is 22/54, or 0.407 of the way from 33 to 34

A good guess for x is 3.407

Logarithm:

3x=72

log3x=log72

x(log3)=2(log7)