Free Printable alg 2 properties of logs

1.

The logarithmic equation $Log_ba=x$ can be rewritten as....

a)

$b=a^x$

b)

$a=b^x$

c)

$x=a^b$

2.

$Log_32x=5$ can be rewritten as...

a)

$2x=3^5$

b)

$5=3^{2x}$

c)

$2x=5^3$

3.

$Log_{6x}4=-9$ can be rewritten as...

a)

$4=6x^{-9}$

b)

$6x=4^{-9}$

c)

$4=-9^{6x}$

4.

$Log4x=2$ can be rewritten as...

a)

$4x=10^2$

b)

$2=10^{4x}$

c)

$10=4^{6x}$

5.

$Log_2\left(2x^2-7\right)=\left(5x+1\right)$ can be rewritten as...

a)

$\left(2x^2-7\right)=2^{\left(5x+1\right)}$

b)

$\left(5x+1\right)=2^{\left(2x^2-7\right)}$

c)

$2=\left(5x+1\right)^{\left(2x^2-7\right)}$

6.

$Log\left(4x^2-3x+8\right)=\left(x-9\right)$ can be rewritten as...

a)

$\left(4x^2-3x+8\right)=10^{\left(x-9\right)}$

b)

$\left(x-9\right)=10^{\left(4x^2-3x+8\right)}$

c)

$10=\left(x-9\right)^{\left(2x^2-3x+8\right)}$

7.

Rewrite the logarithmic equation. $\log_3p=4$

a)

$4^p=3$

b)

$4^3=p$

c)

$p=3^4$

d)

$p^4=3$

8.

Rewrite the logarithmic equation. $\log_x23=2$

a)

$x^{23}=2$

b)

$23^2=x$

c)

$23=x^2$

d)

$23^{x\ }=2$

9.

$\log\left(\frac{1}{81}\right)=-4$ Rewrite the logarithmic equation.

a)

$\frac{1}{81}=10^{-4}$

b)

$81=10^{\frac{1}{4}}$

c)

$4^{10}=\frac{1}{81}$

10.

$Log3x=2$ can be rewritten as...

a)

$3x=10^2$

b)

$2=10^{3x}$

c)

$10=4^{3x}$

11.

$Log_{12}\left(x^2-2x+1\right)=\left(x-5\right)$ can be rewritten as...

a)

$\left(x^2-2x+1\right)=12^{\left(x-5\right)}$

b)

$\left(x^2-2x+1\right)=\left(x-5\right)^{12}$

c)

$\left(x-5\right)=12^{\left(x^2-2x+1\right)}$

12.

$Log_{\left(x+1\right)}\left(2x+1\right)=7$ can be rewritten as...

a)

$\left(2x+1\right)=\left(x+1\right)^7$

b)

$\left(x+1\right)=\left(2x+1\right)^7$

c)

$\left(2x+1\right)=7^{\left(x+1\right)}$

13.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

14.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

15.

$\log\left(\frac{x}{y}\right)$

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

16.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

17.

ln(4xy)

a)

ln4+lnx+lny

b)

4lnxy

c)

4lnx+lny

d)

4ln(x+y)

18.

$\log\left(\frac{9}{4}\right)$

a)

log9+log4

b)

log(9-4)

c)

log9-log4

d)

4log9

19.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

20.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

21.

Expand: $\log_b\ \frac{m}{n}$

a)

$\log_bm\ -\log_bn$

b)

$\log_bm\ +\ \log_b\ n$

c)

$m\log_bn$

d)

$n\log_bn$

22.

Expand: $\log_2\ \frac{5}{x}$

a)

$\log_25\ +\ \log_2x$

b)

$\log_2x-\log_25$

c)

$\log_25-\log_2x$

d)

$5\log_2x$

23.

Expand: $\log\ \frac{k}{d}$

a)

$k\log d$

b)

$\log k\ +\ \log\ d$

c)

$\log\ k\ -\ \log d$

d)

$\log d-\log k$

24.

Expand: $\log_7\ y^8$

a)

$\log_7y\ +\ \log_78$

b)

$\log_7y-\log_78$

c)

$8\log_7y$

d)

$\log_78+\log_7y$

25.

Expand: $\log_9\sqrt{23}$

a)

$\frac{1}{2}\log_923$

b)

$\log_9\left(\frac{1}{2}\right)-\log_923$

c)

$\log_9\sqrt{2}+\log_9\sqrt{3}$

d)

$\log_9\ \left(\frac{1}{2}\right)+\log_923$

26.

$\log\left(\frac{9}{4}\right)$

a)

log9+log4

b)

log(9-4)

c)

log9-log4

d)

4log9

27.

Describe the transformation of y = f(x) to the new function
y = f(1/5x)

a)

Horizontal shrink by a factor of 1/5

b)

Vertical stretch be a factor of 5

c)

Vertically shrink by a factor of 1/5

d)

Horizontal stretch by a factor of 5

28.

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

29.

Describe the transformation

-f(x)

a)

shift down

b)

reflect over x-axis

c)

reflect over y-axis

d)

shift right

30.

Which equation below is a quadratic function translated right 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

31.

If the blue function is f(x)=x², then the red function must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

32.

Describe the transformations

$g\left(-x\right)-4$

a)

Reflected across the x-axis

4 Units Left

b)

Reflected across the x-axis

4 Units Down

c)

Reflected across the y-axis

4 Units Left

d)

Reflected across the y-axis

4 Units Down

33.

Describe the transformation

$h\left(\frac{1}{3}x\right)$

a)

Vertically Stretched by a factor of $\frac{1}{3}$

b)

Vertically Compressed by a factor of $\frac{1}{3}$

c)

Horizontally Stretched by a factor of $\frac{1}{3}$

d)

Horizontally Stretched by a factor of $\frac{1}{3}$

34.

Describe the transformation

$3h\left(x\right)$

a)

Vertically Stretched by a factor of 3

b)

Vertically Compressed by a factor of 3

c)

Horizontally Stretched by a factor of 3

d)

Horizontally Stretched by a factor of 3

35.

Describe the transformations

$-g\left(x\right)+2$

a)

Reflected across the x-axis

2 Units Up

b)

Reflected across the x-axis

2 Units Down

c)

Reflected across the y-axis

2 Units Up

d)

Reflected across the y-axis

2 Units Down

36.

Describe the transformation

$f\left(x\right)-6$

a)

6 Units Up

b)

6 Units Down

c)

6 Units Left

d)

6 Units Right

37.

Describe the transformation

$f\left(x+5\right)$

a)

5 Units Up

b)

5 Units Down

c)

5 Units Left

d)

5 Units Right

38.

Describe the transformation

$f\left(x-2\right)$

a)

2 Units Up

b)

2 Units Down

c)

2 Units Left

d)

2 Units Right

39.

Describe the transformation

$f\left(x\right)+3$

a)

3 Units Up

b)

3 Units Down

c)

3 Units Left

d)

3 Units Right

40.

Which equation describes the transformation of shifting f(x)=x² two units right?

a)

x² + 2

b)

x² - 2

c)

(x + 2)²

d)

(x - 2)²

41.

The exponential function f(x)=2^x and the logarithmic function g(x)=log₂(x) are inverses. You know that because their graphs are reflected over what line?

a)

the x-axis

b)

the y-axis

c)

y=x

d)

y=-x

42.

The inverse of an exponential function is its reflection across the x-axis.

a)

True

b)

False

43.

A logarithmic function is the inverse of an exponential function.

a)

True

b)

False

44.

Are these inverse functions

a)

no

b)

yes

c)

no way to tell

45.

Will the inverse of this function, be a function?

a)

No

b)

Yes

c)

No way to tell

46.

Are these the graphs of two inverse functions?

a)

Yes

b)

No

c)

No way to tell

47.

Are the blue and red graphs inverse functions?

a)

yes

b)

no

c)

no way to tell

48.

The inverse has been reflected over which line?

a)

y = x

b)

x = 0

c)

y = 0

d)

x = -y

49.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

50.

Are these equations inverses?

a)

Yes

b)

No

51.

Is the inverse of the graph a function?

a)

Yes

b)

No

52.

Is the inverse of the graph a function?

a)

Yes

b)

No

53.

Which graph is the inverse of the graph shown?

a)

b)

c)

d)

54.

Which graph is the inverse of the graph shown?

a)

b)

c)

d)

55.

Which graph is the inverse of the graph shown?

a)

b)

c)

d)

56.

Is the inverse of the table a function?

a)

Yes

b)

No

57.

Which is the inverse of the table?

a)

b)

c)

d)

58.

Which is the inverse of the table?

a)

b)

c)

d)

59.

Which is the inverse of the table?

a)

b)

c)

d)

alg 2 properties of logs

Total questions: 59

Worksheet time: 2hrs 44mins

Similar Resources on Wayground