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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
= −