Alg 3 Functions 1

Algebra 3 Assignment Sheet

Functions, Fog, Gof, Inverse, Logs

(1) Assignment # 1 – Functions, Domains

(2) Assignment # 2 – Composition of Functions

(3) Assignment # 3 – Inverse Functions

(4) Review Sheet

(5) Quiz

(6) Assignment # 4 – Exponential Equations

(7) Assignment # 5 – Logarithms

(8) Assignment # 6 – Laws of Logarithms

(9) Assignment # 7 – Laws of Logarithms

(10) Assignment # 8 – Calculator Logarithms

(11) Review Sheet

(12) TEST

Alg 3 Functions 2

Functions

I Vocabulary

a) Function: The set of (x, y) pairs such that____________________________________

____________________________________________________________

b) domain:

c) range:

Vertical Line Test

II Functions ? Y/N Domain

A. a) (2,4) (8,1) (8,8) _____ ______________

b) (1,-2) (3,4) (5,-2) _____ ______________

c) 2y x 5x 6= + + _____ ______________

d) y = |x| _____ ______________

e) 2y = 8 _____ ______________

f) y x= _____ ______________

g) ( )2y = - x + 2 _____ ______________

h) 2

2xf (x)

x 4=

− _____ ______________

f(x) is the same as y

Alg 3 Functions 3

III Restrictions

1) Denominator ≠ 0 5+ x

x,

2 -3x

x -5,

2

x

x +5x - 6

≠x ≠x ≠x

2) for even roots: negative number

Find the domain of the following please.

a) f (x) x 2= − b) f (x) 2x 5= + c) x

f (x) x 2

=−

d) 2y = x x 12− − e) 2

2

x 2x 63y =

x 8x 15

− −+ +

Alg 3 Functions 4

IV Evaluating functions for y when given a value of x

Evaluating: Substituting in numbers y = f(x)

( )

( ) ( ) ( )

2

2

2

2

2 3

(2) 2 2 2 3 11

1 1 2 1 3 2

( ) 2 3

y x x

f

f

f x x x

= + +

= + + =

− = − + − + =

= + +

2( ) 2 3f x x x= + +

1)

f(-1) =

f(0) =

2) = − +2g(x) x 2x 3

Find g(x + 2)

3) If f(x) = 2 3 1− +x x g(x) = x - 5

a) find f(x + 2) b) find 3f( x) • g(2x)

c) find f(g(x))

2f (x) x 2x 3= + +

1f =

2

Alg 3 Functions 5

Algebra 3 Assignment # 1

(1) ( ) 4 3 2f x = 3x 16x 7x 28x 13− − − − , ( ) 2

g x = x + 2x 4− . Find each of the following.

(a) ( )g 4 (c) ( )( )f g 3−

(b) ( )f 6 (d)

(2) Determine whether each of the following defines y as a function of x. If it is a function, find the domain

please.

(a) y 5x 4= − (f) y 5 4x = −

(b) 2

y x + 2x 3= − (g) 2

y x 5x 6 = − −

(c) 2 2x + y = 1 (h)

2

xy

x + 1=

(d) 3x + 5

y 2x 3

=−

(i) 5 2x

y 3x + 4

−=

(e)

3

3

x + 8y =

x 7x + 6− (j)

3 2y x 9x + 23x 15 = − −

(3) Let the function f be defined by ( )f x = x + 1. If ( )2 f = 20ϑ , find ( )f 3ϑ .

(4) Let the function f be defined by ( )f x = x + c , where c is constant. If ( )f 2 = 10 , find the value of the

constant c.

The remainder when ( )f x is

divided by ( )x i−

Alg 3 Functions 6

Answers

(1) (a) 20 (c) 27

(b) –1 (d) –3 – 12i

(2) (a) Real (f) 54

x ≤

(b) Not a function (g) x 1 or x 6≤ − ≥

(c) Not a function (h) Real

(d) 32

x ≠ (i) 543 4 x − ≤ ≤

(e) x 1 , 2 , 3≠ − (j) 1 x 3 or x 5≤ ≤ ≥

(3) 28 (4) 8

Alg 3 Functions 7

Composition of Functions

Functions can be added, subtracted, multiplied and divided.

EXAMPLES

1. If 2f (x) x 3= − and 1

g(x)x

= find

a) f(x) + g(x) b) f(x) g(x) c) f(x) ÷ g(x)

d) f(3) g(3) e) f(3) ÷ g(3)

Notes: Let 3f (x) x and g(x) = x 3= −

f g (x) = f(g(x))�

Use composition to find the following:

If 2f (x) x 3= − and 1

g(x)x

= find

a) f (x) g(x)� b) g(x) f (x)�

If 2 1f (x) 2x 1, g(x)=x and h(x)=

3x= − find f g h(x)� �

Alg 3 Functions 8

If x 6 x+1

f (x) and g(x)=x 4 x+5

−=

− find f g�

DOMAIN:

( ) ( )2f x x 8x 15 , and g x x 3. = + + = +

If 2

1f (x) x and g(x)=

x 2=

− find the domain of g f�

Find all values of x such that ( )( ) ( )( )f g x g f x= if

Alg 3 Functions 9

Algebra 3 Assignment # 2 Composition of Functions

(1) Find each of the following numbers, given the functions below.

( ) 1 2x xf −= ; ( ) 2 x 2x xg 2 −−= ; ( ) 1 x xh 2 +=

(a) ( )( )2hf (b) ( )( )1hg

(c) ( )( )25fg (d) ( )( )( )3gfh

(2) Find ( )( )xgf and ( )( )xfg for each of the following please.

(a) ( )( ) 5 4x xg

1 2x 3x xf 2

−=

−+= (b)

( )

( )1 3x

2 x xg

3 4x

5 2x xf

−+

=

−+

=

(3) Find ( )xg if ( )5 2x

1 3x xf

+−

= , and ( )( )11 12x

9 x xgf

−+

= .

(4) Find ( )( )xff if ( )2 3x

3 2x xf

−+

=

(5) Find all values of x such that ( )( ) ( )( )xfg xgf = if ( ) ( ) 2. 3x xg and , 2 3x 2x xf 2 −=+−=

Alg 3 Functions 10

Answers

(1) (a) 3 (b) 4

(c) 89 (d) 26

(2) (a) ( )( ) 64 112x 48x xgf 2 +−= (b) ( )( )11 x5

1 17x xgf

+−−

=

( )( ) 9 8x 12x xfg 2 −+= ( )( )18 2x

1 10x xfg

+−

=

(3) ( )3 2x

2 x xg

−+

=

(4) ( )( )xff = x

(5) x = 1

Alg 3 Functions 11

Inverse functions ( 1f and f − ) 1f − is not 1

f

NOTES:

A. If f(x) and g(x) are inverses of each other

then f(g(x)) = x and g(f(x)) = x

(they must be one to one to be inverses)

Ex. If f(x) = 2x - 3 g(x) = x 3

2

+

x 3 x 3

f 2 32 2

+ + = − = x + 3 – 3 = x

f(x)

[ ] ( )2x 3 3 2xg 2x 3

2 2

− +− = = = x

g(x)

Alg 3 Functions 12

If 2f (x) x and g(x) = x= , Prove f(x) and g(x) are inverses of each other

B. Finding inverses

• Switch the domain “x” and the range “y”

• Then solve for “y”

EX. f(x) = 2x - 5 y = 2x – 5 switches to x = 2y – 5

solve x 5

y2

+= this is the inverse

Ex. Find 1f − if ( )f x 3x 2= − Domain restrictions become:

Alg 3 Functions 13

V Practice Find 1f − (x) for each of the following:

a) ( ) 3f x x 1= +

b) ( ) ( )2f x x 2 3= + −

c) ( ) 5x 1f x

2

−=

Find ( )( ) ( )( )f g x and g f x for each of the following:

e) ( )( )f x 4x 3

g x x 6

= −

= + f)

( )( ) 2

f x x 3

g x x 2x 4

= +

= + −

Find each of the following numbers, given the functions below:

( ) ( ) ( )2 2f x x 4 , g x 3x x 2, h x x 2= + = − + = −

g) ( )( )f h 4 h) ( )( )g h 2−

j) ( )( )h f 0

Alg 3 Functions 14

Algebra 3 Assignment # 3 Inverse Functions

(1) Find ( )xf 1− for each of the following please.

(a) ( ) 3 5x xf += (e) ( ) 7 5x xf −=

(b) ( )x

4 xf = (f) ( ) 2 5 4x xf ++−=

(c) ( )2 5x

2 3x xf

−+

= (g) ( ) 3 5 4x xf +=

(d) ( )7 2x

2 7x xf

−+

= (h) ( ) 2 8 5x xf 3 −+−=

(2) ( )3 2x

5 6x xf

++

= , ( )( ) x xfg = . Find ( )xg .

(3) ( ) 2 x xf −= . Find ( )xf 1−, and sketch a graph of ( )xf and ( )xf 1−

on the same set of axes.

Alg 3 Functions 15

Answers

(1) (a) ( )xf 1− =

5

3 x − (e) ( )xf 1−

= 5

7 x 2 +

(b) ( )xf 1− = x

4 (f) ( )xf 1−

= 4

1 4x x 2 −−

(c) ( )xf 1− =

3 5x

2 x2

−+

(g) ( )xf 1− =

4

5 x3 −

(d) ( )xf 1− =

7 2x

2 x7

−+

(h) ( )xf 1− =

( )5

8 2 x 3 ++−

(2) ( )xg = 6 2x

5 x3

−+−

Alg 3 Functions 16

Algebra 3 Review Worksheet

(1) Find each of the following numbers, given the functions below.

( ) 2x x xf 2 −= ; ( ) 3x xg = ; ( ) 1 x xh +=

(a) ( )( )3hf (b) ( )( )0hg

(c) ( )( )( )8ghf (d) ( )( )( )8hfg

(2) Find the domain of each of the following functions please.

(a) ( ) 2f x = 24x 29x 4 − − (b) ( )

2

x 1 f x =

x 9

−

−

(c) ( )3 2

5x + 2f x =

x 4x + x + 6− (d) ( ) ( )( )

( )

2 x + 3 x 1

f x = x 5

−

−

(3) Find ( )( )xgf and ( )( )xfg for each of the following.

(a) ( )( ) 3 x xg

1 2x xf

2 −=

+= (b)

( )

( )1 2x

1 x xg

2 3x

3 2x xf

−+

=

−+

=

(4) Find ( )xf 1− for each of the following.

(a) ( ) 7 5x xf −= (b) ( ) 4 5 x2 xf 3 −+=

(c) ( )5 2x

2 3x xf

−

+= (d) ( ) 1 x5 xf +−=

(5) Find all values of x for which ( )( ) ( )( )xfg xgf = if ( ) 5 x xf −= and ( ) 3 4x 2x xg 2 +−= .

(6) Find ( )xg , if ( )2 x

1 2x xf

++

= and ( )( )1 3x

1 6x xgf

+

−= .

Alg 3 Functions 17

Answers

(1) (a) 0 (b) 3

(c) 15 (d) 9

(2) (a) 1 48 3

x or x ≤ − ≥ (b) x 1 and x 3≥ ≠

(c) x 1 , 2 , 3≠ − (d) x 3 or x = 1 or x > 5≤ −

(3) (a) ( )( ) 5 2x xgf 2 −= , ( )( ) 2 4x 4x xfg 2 −+=

(b) ( )( )5 x

1 8x xgf

+−

−= , ( )( )

8 x

1 5x xfg

+

+=

(4) (a) ( )5

7 x xf 1

+=−

(b) ( ) ( )2

5 4 x xf

31 −+

=−

(c) ( )3 2x

2 5x xf 1

−

+=−

(d) ( )5

1 x xf2

1 −=−

(5) 4

15 (6) ( ) 1 3x xg −=

Alg 3 Functions 18

Exponents

I Review

x yb b = ( )yxb =

x

y

b

b=

0b =

xb− = x xb c =

3 3b b = ( ) 23b =

3

2

b

b=

II x yIf b b , then x y= =

x xIf b a , then b a= =

Ex. x 2 53 3+ = Ex.

x 42 2

3 3

=

x+2 = 5 x = 4

x = 3

2

2 2

x 1

x 16

2x 1

x

x 1

x x x 5

1) 2 32

2) 2 2

3) 8 64

14) 642

15) 27

9

6) 8 4

−

+

+

− +

=

=

=

=

=

=

Alg 3 Functions 19

+

+ + =

⋅ + =

+ + + =

x x x

x x

x x x x 1

17. 3 3 3

729

8. 5 4 4 96

9. 3 3 3 3 54

III Sketching

xy 2= 1) NO negative bases

2) (0,1) on every graph

3) b ≠ 1

xy 2−=

-3

-2

-1

0

1

2

3

x y

-3

-2

-1

0

1

2

3

x y

Alg 3 Functions 20

Algebra 3 Assignment # 4

Exponential Equations

(1) Solve for x please.

(a) x1 x 8 4 =+ (b) 5

2513 x =+

(c) 7 x 1 x2 8 2 −− = (d)

1 x2x x 2227 9 +− =

(e) ( ) 41 ••••

x 11 x2 16 8 −− = (f) ( ) 16 1 x 34 2 =−

(g) 827 x 2

3

=−

(h) 13 2 x2 − •••• 0 48 2x =−

(i) 10 27 x2 − •••• 0 9 27x =+ (j) 10 16x − •••• 0 16 4x =+

(2) Sketch a graph of each of the following.

(a) x3 y = (b)

x3 y −=

Alg 3 Functions 21

Answers

(1) (a) 2 (b) −5

(c) 20 (d) −1 , −3

(e) 910 (f) ± 3

(g) 94 (h) 4

(i) 0 , 32 (j)

2

3

21 ,

Alg 3 Functions 22

EXPONENTIAL EQUATIONS EXTRA

(1) Evaluate each of the following numbers please.

(a)

3 12 29 49

−i (c)

2 2 22 4

−i

(b)

2 2

1

2 + 2

2

−

− (d)

1

3 2

2 2 3

−

− −−

(2) Solve each of the following equations please.

(a)

23x = 25 (e) ( )

32 5x + 7 = 8

(b)

35 1

x = 8

− (f) ( )

32 4x 6x + 9 = 27−

(c) 2x + 3 x + 48 16= (g)

2x x8 6 8 + 8 = 0− i

(d) ( )2x + 1 x 314

8 = 16−

i (h)

3x3x 24 9 4 + 8 = 0− i

(3) Sketch a graph of each of the following on the same set of axes.

x

y = 2 and ( )2y = xlog

Alg 3 Functions 23

Answers

(1) (a) 277 (c) 1

(b) 172 (d) 6

(2) (a) 125 (e) 5±

(b) 32 (f) 12 , –6

(c) 72 (g) 1 2

3 3 ,

(d) 138 (h) 0 , 1

Alg 3 Functions 24

LOGS

Logs are the inverse of exponential functions.

If y = 2x + 3 to find inverse

x 2y 3

x 3y

2

= +

−=

If xy 2= to find inverse

yx 2=

How do you solve for y?

Logarithms are exponents and follow exponent rules.

EXPONENTIAL FORM LOGARITHM FORM

33 27= 3log 27 3=

2 1

525

− = 5

1log 2

25= −

32 8= 2log 8 3=

x4 1= 4log 1=

RULES

base

power number

blog n p= pb n=

base

power number

Alg 3 Functions 25

EXAMPLES

3

2

5

8

6

log 81 x

log 4 y

log 25 z

log 16 p

log 6 a

=

=

=

=

=

( )

8

27

9 3

125

log 1 c

log 9 d

1log log x

2

2log x

3

=

=

=

= −

warm-up before next lesson

1)

2

2 4

2

5 2−

-

- -

2) ( )2148

−x + 1 x 3 = 16i 3)

3x3x 24 9 4 + 8 = 0− i

4) 2

3

8log =

27 5)

b

1 3log =-

27 2 6)

3 1

4 27

1

81=log (log ) x

7) 10 =.001log y

Alg 3 Functions 26

Algebra 3 Assignment # 5 Definition of the logarithm

Solve for x please.

(1) ( ) x 64 log4 = (10) ( )3 2 = x5ln e

(2) ( ) 2 x log6 = (11) ( ) 2 251

xlog −=

(3) ( ) 2 9 logx = (12) ( ) x 216 log36 =

(4) ( ) 2 xlog3 −= (13) ( )23

4 x log −=

(5) ( ) x 125 log25 = (14) ( ) x 24 log8 =

(6) ( )32

8 x log = (15) ( )

21

x 6 log −=

(7) ( ) x 81log27 = (16) ( ) ( )2ln eln e3x = + 54

(8) ( ) x 7 log7 = (17) ( )( )21

24 x loglog =

(9) ( )43

16 x log −= (18) ( )( )

41

x16 9 loglog =

Alg 3 Functions 27

Answers

(1) 3 (10) 103

(2) 36 (11) 5

(3) 3 (12) 23

(4) 91 (13)

81

(5) 23 (14)

65

(6) 4 (15) 361

(7) 34 (16) 33

(8) 21 (17) 4

(9) 81 (18) 3

Alg 3 Functions 28

LAWS OF LOGS

Properties of Logs

I LAWS II Equations

b b b

b b b

pb b

log mn log m log n

mlog log m log n

n

log m plog m

= +

= −

=

III Examples

1) ( ) ( )25 5log 2n 20 log 32 5n+ = −

3) 6 6 6log 48 log w log 4− = 4) 2 2 2log 3 log 7 log x+ =

5) 10 10

1log m log 81

2= 6) 7 7 7

1 1log m log 64 log 121

3 2= +

( )b b

nb

If log m log n then m n

log =log

If log m n then b m

(log number)

= =

= =

=

Alg 3 Functions 29

7) ( )10 10 10log m 3 log m log 4+ − = 8) 6 6 6

12log 4 log 8 log

3x− =

9) 4 4log ( 3) log ( 3) 2x x+ + − = 10) ( )2 2log ( 2) 1 log 2y y+ − = −

11) 3 3 7log log 5 log 7− =x 12) 2 2 3log ( 1) log (3 1) log 243+ + − =x x

Alg 3 Functions 30

Algebra 3 Assignment # 6 Logarithmic Equations

(1) Evaluate each of the following please.

(a) ( )7log 6

7 (b) ( )25log 36

5

(c) ( ) ( )8 4log 27 log 25

4 + 8 (d) ( ) ( )2ln 8 3ln 4

e−

(2) Solve for x please.

(a) ( ) ( )3 32x 1 3x 6log log+ = − (b) ( )2

10x + 9x = 1log

(c) ( ) ( )5 5x = 4 3log log (d) ( ) ( ) ( )1 1

9 9 92 3x = 144 8log log log−

(e) ( ) ( ) ( )3 3 37 + x 2 = 6xlog log log− (f) ( ) ( ) ( ) ( )15 + 14 105 = xln ln ln ln−

(g) ( ) ( ) ( )10 10 7x 1 + x + 2 = 7log log log− (h) ( ) ( ) ( )3 3 3

x + 3 + x 3 = 16log log log−

(i) ( ) ( ) ( )8 8 8x + 1 x = 6x + 2log log log− (j) ( ) ( ) ( )3 3 3

x + 3 + 4x 1 = 12log log log−

(k) ( ) ( )2 28 8 3x x 2x 5 = log log− − − (l) ( ) ( )4 9log logx 9 4 = 125 8 3−

Alg 3 Functions 31

Answers

(1) (a) 6 (b) 6

(c) 134 (d) 1

(2) (a) 7 (b) 10 , 1−

(c) 9 (d) 6

(e) 14 (f) 2

(g) 3 (h) 5

(i) 13 (j) 1

(k) 4 , 5 (l) 23

Alg 3 Functions 32

Algebra 3 Assignment # 7 Logarithmic Equations

Solve for x please.

(1) ( ) ( )2 14 4 2x 1 5x 11 = log log− − −

(2) ( ) ( ) ( )26 6 63x 5 x 1 = x 1log log log− − − −

(3) ( ) ( ) ( )24x + 1 + x + x = 19x 9ln ln ln −

(4) ( ) ( )2 2 28 8 33x 7 x x 1 = log log− − − −

(5) ( ) ( ) ( )2x + 4 + 3x 4 = 17x 18ln ln ln− −

(6) ( ) ( ) ( ) ( )92ln 3 log 25

2 2x + 1 + x 5 = e 3log log − −

(7) ( ) ( )3 9x 5 = x + 7log log−

(8) ( )( ) ( )2

8 83 x x 2 = 0log log− −

(9) ( )( ) ( )2

4 42 x + x = 0log 5log

(10) ( )22 x = 3ln −

Alg 3 Functions 33

Answers

(1) 3 , 7

(2) ( )2 , 3 , reject 5−

(3) ( )34

1 , , reject 3−

(4) 3 , (reject 1)

(5) ( )132 , reject 1 , −

(6) 7 , (reject 3)−

(7) 9 , (reject 2)

(8) 14

8 ,

(9) 132 , 1

(10) Ø

Alg 3 Functions 34

Algebra 3 Assignment # 8 Calculator Logarithm Problems

(1) Use a calculator to solve each of the following correct to 4 decimal places please.

(a) x5 = 20 (b)

3x + 1 1 x4 = 9 −

(c) ( )318 = xlog (d) ( )7

x = 1.432log

(e) ( )x = 1.432ln (f) ( )3xlog

5 = 11

(g) x0.3 > 7 (h) ( )( ) ( )2

2 x 5 x 3 = 0ln ln− −

(2) Let ( )102 = plog and ( )10

3 = qlog . Evaluate each of the following in terms of p and q.

(a) ( )106log (b) ( )10

72log

(c) 10 5

3 3

16log

(d) ( )1090log

(e) ( )100.5log (f) ( )10

5log

(3) Simplify the following expression please.

( ) ( ) ( )4 49 25125 32 7 log log logi i

(4) The magnitude of an earthquake is measured using the Richter scale;

4.4

2 EM =

3 10log

,

Where M is the magnitude of the earthquake, and E is the seismic energy released by the earthquake (in

joules). The 1989 San Francisco earthquake released approximately 151.12 x 10 joules. Calculate the

magnitude of the earthquake using the Richter scale. How much energy would be released (in joules) by an

earthquake which measures 8.3 on the Richter scale?

Alg 3 Functions 35

Answers

(1) (a) 1.8614 (b) 0.1276

(c) 2.6309 (d) 16.2248

(e) 4.1871 (f) 5.1388

(g) x < −1.6162 (h) 0.6065 , 20.0855

(2) (a) p + q (b) 3p + 2q

(c) 3 42 5q p− (d) 2q + 1

(e) −p (f) 1 − p

(3) 158

(4) 7.1 , 167.079 x 10 joules

Alg 3 Functions 36

Algebra 3 Review Worksheet

(1) Solve for x please.

(a) 2–x 2x+19 = 27 (i)

( )9log 49 = x

(b) 2x–5 x+18 = 16 (j)

( ) ( )9 3log 4 log 43 – 9 = x

(c) ( ) 1–x2x 116

4 8 = i (k) ( )28 83 log (x) – 2 log (x) – 1 = 0

(d) ( )38log 4 = x (l) ( ) ( )5 5 log 2x 3 = log 1– x+

(e) ( )14

1log x = –

2 (m) ( ) ( )2 2log x 1 + log 3x–1 = 5+

(f) ( )x4

log 16 = –3 (n) ( ) ( ) ( )2 2 2log x – 3 – log x+1 = log 8

(g) ( )xlog .125 = 3 (o) ( ) ( ) ( ) ( )7 7 7 7log x 1 + log x + log 2x 1 = log 30+ +

(h) ( )( )3 8log log x = –1 (p) ( ) ( ) ( )24 4

log 6log 2 log x4 + 4 = 8

(2) Use a calculator to solve for x. Express answers correct to 3 decimal places.

(a) x3 = 8 (b)

3x–2 1–x2 = 5

(c) ( )3log 2 = x (d) ( )( ) ( )3x 4 x = 0ln ln−

Alg 3 Functions 37

Answers

(1) (a) 8

1 (i) 4

(b) 2

19 (j) –14

(c) –3 (k) 8 , 2

1

(d) 9

2 (l)

3

2–

(e) 2 (m) 3

(f) 8

1 (n) ∅

(g) 2

1 (o) 2

(h) 2 (p) 4

(2) (a) 1.893 (b) 0.812

(c) 0.631 (d) 1 , 7.389 , 0.135

Alg 3 Functions 38

Algebra 3/Trig Extra Optional Review – B. Solve for x:

1. − +=2 x 2x 19 27 2. ( ) +− =

x 12x 58 2 3.

−

⋅ =

1 x

2x 14 8

16

4. =38log 4 x 5. = −1

4

1log x

2 6. = −x

1log 2

2

7. =xlog (0.125) 3 8. = −3 8log (log x) 1 9. =9log 49 x

10. − =9 3log 4 log 43 9 x 11. − − =2

8 83(log x) 2 log x 1 0

12. + = −5 5log (2x 3) log (1 x) 13. 3log (1 x) log (1 2x) log 3− + − =

14. − − + =2 2 2log (x 3) log (x 1) log 8 15. 4 2log (2x 3) log x+ =

16. + =4 42log 2 log xlog 64 4 8 17. + + + + =7 7 7 7log (x 1) log x log (2x 1) log 30

C. Isolate x completely.

1. =x3 8 2. − −=3x 2 1 x2 5 3. + +=2x 3 x 15 3

Alg 3 Functions 39

ANSWERS

B. 1. 1

x8

= 2. =31

x11

3. x = -3 4. 2

x9

=

5. x 2= 6. 1

x4

= 7. 1

x2

= 8. x 2=

9. x 4= 10. x = -14 11. 1

x ,82

= 12. 2

x3

= −

13. 3

x2

= − 14. No solution 15. x = 3 16. x = 4

17. x = 2 (the other 3 are imaginary)

C1. log8

1.893log3

= 2. log20

.812log40

= 3.

3log125

1.75925

log3

= −