Free Printable Unit 9 Test

1.

Rewrite the logarithm in exponential form:
$\log_yx=10$

a)

$y^{10}=x$

b)

$x^{10}=y$

c)

$10^y=x$

d)

$y^x=10$

2.

log15=x

a)

$1^x=15$

b)

$0^x=15$

c)

$15^x$

d)

$10^x=15$

3.

Write the following logarithm as an exponential:
$\ln\left(5\right)=x$

a)

$5^x$

b)

$e^x=5$

c)

$e^5=x$

d)

$x^5=2.71$

4.

Solve $2^x=13$
Round your answer to the nearest 100th

a)

1.11

b)

0.27

c)

3.70

d)

3.60

5.

Solve $\frac{5^x}{3}=2$
Round to the nearest 100th

a)

1.11

b)

0.79

c)

0.90

d)

1.28

6.

Expand.

a)

1/3 log x + log y + log z

b)

1/3 log x + 1/3 log y + 1/3 log z

c)

1/3 log x - 1/3 log y - 1/3 log z

d)

3 log x + 3 log y + 3 log z

7.

Expand.

a)

log x + 5 log y

b)

5 log x + 5 log y

c)

5 log x - log y

d)

log x - 5 log y

8.

Condense to a single logarithm.

a)

ln x⁴/ y

b)

ln xy⁴

c)

ln x/ y⁴

d)

ln x⁴/ y⁴

9.

Condense.

a)

log₂x²y¹⁰

b)

log₂x²+log₂y¹⁰

c)

log₂x²/y¹⁰

d)

log₂10xy

10.

Evaluate.

a)

-2

b)

2

c)

6

d)

-6

11.

Rewrite the exponential equation. $4^3=64$

a)

$\log_364=4$

b)

$\log_464=3$

c)

$\log_34=64$

d)

$\log_43=64$

12.

Rewrite the exponential equation. $x^2=17$

a)

$\log_x17=2$

b)

$\log_x2=17$

c)

$\log_217=x$

d)

$\log_x2=17$

13.

Rewrite the logarithmic equation. $\log_x23=1$

a)

$x^{23}=1$

b)

$23^1=x$

c)

$x^1=23$

d)

$23^{x\ }=1$

14.

Solve: 9^8-x = 27^x-3

a)

5

b)

-5

c)

1/5

d)

-1/5

15.

Solve for x:
2^{3x + 1} = 32

a)

0

b)

-1

c)

5/3

d)

4/3

16.

Solve:
log x + log 8 = 2

a)

10

b)

12.5

c)

15

d)

17.5

17.

Where is the asymptote for y=log (x-2)?

a)

y=2

b)

y=-2

c)

x=2

d)

x=-2

18.

How are exponential and log functions related?

a)

They are cousins

b)

They are siblings

c)

They are married

d)

They are inverses

19.

Match the graph with its equation

a)

y = log₄ (x)+2

b)

y = log₄ (x + 2) + 1

c)

y = log₄ (x - 1) + 2

d)

y = log₄ (-x + 2)

20.

What is the horizontal asymptote and what transformations have taken place?
y = 2^x+2 + 1

a)

y = 2
right 2, up 1

b)

y = 1
left 2, up 1

c)

y = 1
right 2, up 1

d)

y = 2
right 1, up 2

21.

What is the Vertical Asymptote?

a)

x=5

b)

x=0

c)

y=0

d)

x=1

22.

Solve: 9^8-x = 27^x-3

a)

5

b)

-5

c)

1/5

d)

-1/5

Unit 9 Test

Total questions: 22

Worksheet time: 55mins

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