## Description

Hi there! This assignment is about exponents and logarithms. Please show all your work. I dont mind in which format the assignment is completed, you can print it and work on it or do it through a program online. Msg if you have any questions, thanks!

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## Explanation & Answer

Hi Danica. Please see attached file.

WCLN PCMath 12 - Rev. 2019

Name: _______________________________

UNIT 4 - LEARNING GUIDE: Logarithms

Instructions:

Using a pencil, complete the following questions as you work through the related lessons. Show

ALL work as it is explained in the lessons. Do your best and ask your instructor if you do not

understand any questions!

Lesson 1 – Review the Exponent Laws

1. Simplify the following and write answers with positive exponents only.

a)

(x 2 )4

x −3

b)

= x (2∗4 − −3)

= m(−2−3) n(−3−1)

= x11

=

2

x 2∗2 x

= 2 ∗ 3

y

2y

=

g)

x 4+1

x5

=

2y 2+2 2y 5

(xy)2

1

m5 n4

e)

9y 6 2

( 2 ) ÷ xy

4x

1

=

1

42 x

=

1

2−2 x −2

33 x (2∗3)

=

1

1

=

4 ∗ 27 ∗ x (2+6) 108x 8

(3m)−1 n 3

( )

(2n)2 m2

1

n3

=

∗

3 ∗ 22 ∗ mn2 m2∗3

1

1∗

xy

2∗

2

3y 3 1

3y 2

∗

=

2x1 xy 2x 2

x2y2

2x 3

1

=

∗(

) ∗ = 22 x 2+2∗3 ∗ y 2−1

1

1

y

(2x)−2

(3x 2 )3

=

f)

92 y 6∗2

1 −2

( 3) ÷ y

2x

2

c)

1

−1

x2

2y 3

d) ( ) (

)

y

x

(m2 n3 )−1

m3 n

=

1

n3

n

∗

=

2

6

12mn m

12m7

2

h)

(2m2 )−1

m 4

(

)

÷

(

)

n3

3n3

2

1

m4

1

81n12 81n6

= ( 2 3 ) ÷ 4 3∗4 =

∗

=

2m n

3 n

4m4 n6

m4

4m8

= 4x 8 y

Page 1 of 19

WCLN PCMath 12 - Rev. 2019

2. Simplify and then evaluate the expressions for x = -1, y = 2, z = 3.

a) (3x 2 y −1 z 2 ) (4x −1 y 2 z )

= 12x

(2xy 3 z −1 )2

x2y4

b)

22 x 2 y 3∗2 z −1∗2

4x 2 y 6 z −2

=

=

x2 y4

x2y4

2−1 −1+2 2+1

y

z

= 12xyz 3

= 22 x 2−2 y 6−4 z −2 =

= 12(−1)(2)(3)3 = −648

=

4y 2

z2

4(2)2 16

=

(3)2

9

Lesson 2 – Solving Equations Involving Exponents

1. Solve for x using the reciprocal of the exponent.

2

a) x 3 = 4

3

2 2

(x 3 )

= 43/2

x=8

3

40

=

=8

5

2

3 3

(x 2 )

x=4

1

(x −2

x=

c) 5x 2 = 40

3

x2

1

b) x −2 = 9

= 82/3

−

)

2

1

2

= 9 −1

1

1

=

2

9

81

2

d) (4x + 1)3 = 25

((4x +

3

2 2

1)3 )

4x + 1 = 125

x =

Page 2 of 19

3

= 252

125 − 1

= 31

4

WCLN PCMath 12 - Rev. 2019

2. Solve for x by converting to common bases. Show all your work.

1 x

x

a) 2 = 32

b) ( ) = 81

C) 5x = 625

3

2 =2

1 x

1 −1

1 −1

1 −4

( ) = ( ) = ( 4) = ( )

3

81

3

3

5x = 54

x=5

x = −4

x=4

d) 3x−2 = 27

e) 42x = 8

f) 27x−1 = 9

x

5

3

3x−2 = 33

42x = 42

x−2 =3

2x =

x=5

x=

g) 3(16x+2 ) = 96

16x+2 =

96

= 32

3

3

4

x=

2x

2x − 1 =

5

3

→ x=−

4

4

j) 4x = 8...