Exponential and Logarithmic Function Lab Answer KEY PDF

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PREPA TEC CEGL MATH III

2st PARTIAL LAB

TOPIC EXPONENTIAL AND LOGARITHMIC FUNCTION

NAME __________________________________________________ ID _____________ Group _______ I. TRUE / FALSE

y = - 3x

1.__FALSE__ The function

is not an exponential function

y = 2x

2.__FALSE__ The graph of the function

passes through the point ( 1, 0 ) , 3.__FALSE__ The range of the exponential function is always the set of Real Numbers 4.__FALSE__ The function y = 3 is the inverse of y = log3 x 5.__FALSE__ The domain of the logarithmic function is the set of Real Numbers x

y = 3 + 5x − 4

6.__FALSE__ The graph of the function

is equal to the graph of the function

y = 5x

shift of 3 units upward and a horizontal shift of 4 units to the left

log3 x y = 2 log 3 x + 4 log3 y 2 4

7. __TRUE__

y = 4- x

8. __TRUE__ The graph of the function

log8 x - log 8 y = 9.__FALSE__ 10. __TRUE__

log 3 7=

is decreasing

log 8 x log 8 y

ln7 ln3

II.- MULTIPLE CHOICE 1.___C__ The value of a)

log 5 log 100

log

5

100

is:

log b)

100 5

2.___A__ The graph of the function a ) y = -2 b) x =- 2

c)

y= 5

x+ 4

− 2

c)y= - 4

log 100 log 5

d)

has an asymptote at: d) x = -4

y = = - log3 x

3.___A__ The graph of the function a )is decreasing c ) has the set of Real Numbers as its domain

4 .___A__ a)x>4

The domain of the function b) x>-4

5. ___B__

The range of the function

a)y>3

b) y>5

b )passes through the point ( - 1, 0 ) d ) has an asymptote at y = 0

y = log2 ( x - 4 ) + 2 c) x>2

y = 2x− 3+ 5 c) y>-3

is: d) x>-2

is: d) y>-5

ln 100 log 5

,

but with a vertical

III. Relate each function with its corresponding graph

1.

1.

y = 4 x +3 + 2

3.

y = log6 ( x - 2 ) + 5

( F

)

5.

1 y = ( )x + 3+ 2 4

(

)

(

D

B

)

2.

y = 5- x − 1

4.

y = log0.5 ( x

6.

y = - log2 x

a)

b)

c)

d)

e)

f)

( E

+ 3) − 4

(

( C

)

A

)

)

IV. Properties of logarithms Use the properties of Logarithms, to expand each logarithmic expression

 y  log 2  x 4 3  z  

Ln

1 4 log 2 x + [ log2 y−3 log 2 z ] 2 4

log2

(

(x−5 )2 4 x ( x−1 )3

)

2 ln ( x −5 ) −4 ln x−3 ln (x−1)

3

 y3 x 4 log3  3 5 2  zw 

w z x3 y8

4 log 2 w+3 log 2 z−(3 log 2 x +8 log 2 y )

   

1 [ 3 log 3 y +4 log 3 x−5 log 3 z−2 log3 w ] 3

Use properties of logarithms, to condense each logarithmic expression.

-

1 1 log5 wz + 4 log5 m log5 x − 3log5 y − 4 2

1  log 8  y 2 log 8  y 4    log 8  y  1  3

y+ 4 ¿ ¿ ¿2 y¿ √3 ¿ log 8 ¿

m4 log 5 √ x y3 √4 wz

2log3 w + 3log3 x −

1 1 log3 x log3 wz + 2 3 w x √x √3 wz 2

log 3

log 2 3+ log 2 ( a−1 )−2 log 2 (a+1)

3

log 2

3 (a−1) (a+1)2

V. Find the value of each expression. Use the change-of-base formula if necessary.

log3 45 =

3.4649

log 10000 =

4

log 0.25 400 = log2 4096 =

-4.3219

12

ln 600 = lne = 1

6.3969

log3 243 =

5

log 10 =

1

log8 1000 =

log 4 =

3.3219

Log0 .75 400 =

.6020

-20.8266

ln 200 =

5.2983

VI. Solve the next exponential and logarithmic equations

e x +6 =e 5 x 2

5

x−2

=

1 125

15 e x−1=100

x=3, 2

x=2.8971

x=-1 2

x 2 −44 x+18

=32

( )

6−8 x

27 8

x=6, -2 X=

x

=

9 4

7 ¿ ¿ 11+2 ¿

2 3 x=2.5395

log 8 ( x−6 )+log 8 (x +6 ) =2

2 log 2 x=3+ log 2 (x−2)

x=10

6 x − 3= 2x

x=4 +2

X=6.1546

ln 2 x + ln 4 =5

log 2 ( 2 x +2) −log 2( x +1 )=3 NO SOLUTION

34 - x = 82x

− 2

x=1.6268 2 log 3 x−log 3 ( x −4 )=2+log3 2

x=12, 6

log ( 3−x )−log ( x+ 9) =0

log 16 x+ log 16 ( x−4 ) = x=18.5516 x=-3

Ln x + Ln (x+1) = 1

5 4

x=8

Ln (x+1) – Ln (x-2) = Ln x ln(30) * 4x+1 =10

x=1.2228

x=3.3027 x=-0.2220

1 −7+ log 2 ( x−6 )=−6 3

log ( x +4 )−log x=log ( x +2)

log ( x−6 )=log(2 x +1)

x=1.5615

x=14

NO SOLUTION

VII. Graph the next exponential and logarithmic functions. Include domain, range, key point and the asymptote.

y = 4x − 3 + 2

y = Log2 ( - x + 3 ) + 2

Domain __(-∞,3)__ Range __(-∞,∞)__ Asymptote __x=3___ Domain __(-∞,∞)____ Range __(2,∞)_ Asymptote __y=2__

y = Log√ 3 ( x + 2 ) - 3

y =

( ) 5 3

-x

− 4

Domain _(-2,∞)_ Range _(-∞,∞)____ Asymptote __x=-2__ Domain _(-∞,∞)____ Range ___(-4,∞)___ Asymptote __y=-4__

y= e

-x + 1

y = -4x − 2+ 2

+1

Domain _(-∞,∞)____ Range __(1,∞)__ Asymptote __y=1__

y = 1 + Log 3( x − 3 )

Domain _(-∞,∞)____ Range __(-∞,2)__ Asymptote __y=2__

y = -Ln ( x+3 )+1

4

Domain __(3,∞)____ Range _(-∞,∞)____ Asymptote __x=3__

Domain __(-3,∞)____ _ Range _(-∞,∞)____Asymptote__x=-3__

VII. Applications of Exponential and Logarithmic Functions 1.A total of $ 6,000 is invested at an annual interest of 4.3 %. Find the balance after 3 years if it is compounded: a) annually

$6807.75

b) continuously

c)monthly

d) daily

$6826.14

$6824.56

$6826.08

2. The population of a certain city is given by P=618 e in years from the year 2000 a)Find the population for the 2005

797.50

0 .051t

where P is measured in thousands of people and “t”

b) Find the population for the year 2020 1713.83

c)Find when the population will be 2 million

Year 2023

3. Suppose that you invest $2000 at an annual interest rate of 17%, compounded continuously. How long will it take your money to be $5000. 5.38 Years...