Unit 5 Review

1

1

This has an exact value:

What is 1/3

1

Solve using Logarithms:

log_(x+2)(16)=2

x=2

1

Convert to Logarithmic Form:

e^(x+4)=2y-7

ln(2y-7)=x+4

1

Solve: 5^x-4=25^x-6

What is 8?

1

Solve for x:

3log(4)-log(x)=log(2)

x=32

2

1

Solve for x:

5^(2x)=21

x=log_5(21)/2

1

If f (x) = −9x − 9 

and 

g(x)=

sqrt(x-9)

find f(g(10))

What is f(g(10))=-18 ?

1

Completely expand the following logarithms. 

log₅4(x)^1/3

log₅4 + (1/3)log₅(x)

1

Solve.

log_4(x)=-5

x=

x = 1/1024

1

Given f(x) = x² and g(x) = x - 4 

What is f(g(x))? Fully simplify your answer

f(g(x)) = (x - 4)²

          =(x -4) (x - 4)

          = x² -4x -4x +16

          = x² -8x +16

3

1

Evaluate the following log. 

log₄(1/64)

-3

1

Given the functions h(x) = 2x - 6 and g(x) = x+ 4

What is h(g(x))

h(g(x)) = 2(x+4) - 6

           = 2x +8 -6

           = 2x + 2

1

This can be written as a single logarithm

What is:

1

Solve for x:

2ln(2)+ln(x)=ln(x+12)

x=4

1

The DOMAIN of the function log(x)

(0, infinity) or x>0 

4

1

Solve for x:

2*3^(x-5)=12

x=log_3(6)+5

1

Solve: log₅(2x-7)=log₅(3x-9)

no solution

1

State the Transformations:

2log(x-3)

2: Vertical Stretch by 2

x-3: Right 3

1

Solve: log₂x+log₂(x-2)=3

4

1

What is the domain of 

ln(x-1)

x>1

or

(1,infinity)

5

1

Convert to Exponential Form:

log_(x-1)(4)=2y

(x-1)^(2y)=4

1

Round to the nearest thousandth.

1.7712

1

Write the inverse function of 

f(x)=4e^x

ln(x/4)

1

Solve for x:

 2*e^(3x-1)-7=13

 x=(ln10+1)/3

1

Find the inverse.

6

1

Evaluate the following log. 

ln(e¹⁰)

10

1

State the transformations:

f(x)=-ln(x-4)+1

-: reflection over the x-axis

x-4: right 4

+1: up 1

1

Inverse Functions

The reason the inverse of the points below is not a function:

(1, 4), (-3, 5), (2, 4), (1, 4)

What is there is more than one output for the input of 4?

1

This can be written as the sum and difference of multiple logarithms:

What is:

1

Given f(t)=

t^2 -t

 and h(x)=3x+2

Evaluate f(h(1))

What is f(h(1))=20 ?