Free Printable Practice logs

1.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

2.

Use multiple log properties to write as a sum or difference of two logs: log(4x³)

a)

log 4 + 3log x

b)

3log 4 + 3log x

c)

3log 4 + log x

d)

log 12 + log x

3.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

4.

Expand: $\log_74\sqrt{d}$

a)

$\log_7\ 4\ -\ \frac{1}{2}\log_7\ d$

b)

$4\log_7d\ +\log_7\ \frac{1}{2}$

c)

$\log_7\ 4+\frac{1}{2}\log_7\ d$

d)

$\frac{1}{2}\log4d$

5.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

6.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

7.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

8.

This question is SLIGHTLY a challenge but you should all be able to do it!!
log x - log 8 = 3

a)

x = 1000

b)

x = 800

c)

x = 8000

d)

x = 100

9.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

10.

Rewrite as a single log:
4 log g - 2 log h

a)

log (4g/2h)

b)

log (g⁴/h²)

c)

log (g⁴ - h²)

d)

log (2gh)

11.

Solve using the properties log₅x - log₅2 = log₅15

a)

6

b)

8

c)

15

d)

30

12.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

13.

Solve $27^{3x}=81$

a)

$\frac{4}{9}$

b)

$\frac{2}{3}$

c)

$1$

d)

$\frac{4}{3}$

14.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

15.

Evaluate log₈ 8

a)

8

b)

-1

c)

0

d)

1

16.

$16=4^{2x-12}$

a)

5

b)

7

c)

2

d)

4

17.

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

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

18.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

19.

log(x⁷)

a)

log(7x)

b)

log7+logx

c)

xlog7

d)

7logx

20.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

21.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

22.

Identify the following function.

a)

Linear

b)

Exponential

c)

Quadratic

d)

Neither

23.

Identify the following function.

a)

Linear

b)

Exponential

c)

Quadratic

d)

Neither

24.

This is a _______________ function.

a)

Linear

b)

Exponential

c)

Quadratic

25.

y=x²

^{What type of equation is the above?}

a)

exponential

b)

linear

c)

quadratic

d)

neither

26.

A(n) _________________ function will MULTIPLY the same number each time.

a)

Linear

b)

Quadratic

c)

Exponential

d)

All of the above

27.

A(n) _________________ function will ADD the same number each time.

a)

Linear

b)

Quadratic

c)

Exponential

d)

All of the above

28.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

29.

Which function is quadratic?

a)

f(x)

b)

h(x)

c)

g(x)

30.

Which kind of function has the same First Differences

a)

Linear

b)

Quadratic

c)

Exponential

d)

Absolute Value

31.

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

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

32.

Solve:
3^x-1 = 81

a)

5

b)

6

c)

9

d)

10

33.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

34.

Solve:

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

35.

$\log_8\left(2\right)=\frac{1}{3}$ In the expression, 8 is the

a)

base.

b)

exponent.

c)

argument.

d)

answer.

36.

Choose the graph that represents a logarithmic function.

a)

b)

c)

d)

37.

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

38.

When you have a log expression with a number in front of it, we really need to ___________ .

a)

make the number an exponent at the end of the log expression.

b)

multiply it with the log expression.

c)

add it to the log expression.

d)

subtract it from the log expression.

39.

When you have two log expressions separated by a plus sign (+), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

40.

$\log27=3\ \log x\$

x=?

(a)

Practice logs

Total questions: 40

Worksheet time: 3hrs 57mins

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