# Ballenas Secondary Exponents and Logarithms Problems Homework

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Mathematics

Ballenas Secondary

## 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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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...

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