Free Printable solve Logarithmic equations

1.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

2.

Solve for x:

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

3.

Solve for x:

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

4.

Solve for x:

log_x1000=3

a)

1

b)

10

c)

30

d)

3

5.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

6.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

7.

Solve

a)

1

b)

-1

c)

6

d)

-6

8.

Solve

a)

1/3

b)

-1/3

c)

-3

d)

3

9.

Solve

a)

-1/4

b)

1/4

c)

4

d)

-4

10.

Solve

a)

1

b)

0

c)

-1

d)

Undefined

11.

log(216)=(x-4)log(6)

a)

1

b)

3

c)

7

d)

0

12.

2log₅7 = 3x+1 log₅49

a)

1

b)

-1

c)

5

d)

0

13.

Solve the equation for x.

a)

22.198

b)

e

c)

1.131

d)

21.66

14.

Solve the equation for x.

a)

7.389

b)

0.693

c)

0.0183

d)

6.581

15.

Expand the logarithm
log₁₀ 7x

a)

(log₁₀ 7)(log₁₀ x)

b)

log₁₀ 7 + log₁₀ x

c)

7log₁₀ x

d)

xlog₁₀ 7

16.

log₂(x²- 6) = log₂(2x+2)

a)

4, -2

b)

No Solution

c)

4

d)

-2

17.

a)

x is undefined

b)

x = 2

c)

x= 0.4

d)

x = 33

18.

a)

x = 5 and x = -2

b)

x = -2

c)

x = 5

d)

x = -10 and x = 10

19.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

20.

Use the properties of logarithms to rewrite as the difference of two logs:

\log_545

a)

$\log_590\ -\log_52$

b)

$\log_515-\log_53$

c)

$\frac{\log45}{\log\ 5}$

d)

$\log_550-\log_55$

21.

Which of the logarithms below is equivalent to the following:
$2\log12$

a)

log 10

b)

log 6

c)

log 24

d)

log 144

22.

Condense this expression to a single logarithm.

a)

b)

c)

d)

23.

Condense this expression to a single logarithm.

a)

b)

c)

d)

24.

Condense this expression to a single logarithm.

a)

b)

c)

d)

25.

Condense this expression to a single logarithm.

a)

b)

c)

d)

26.

$\log_312$
Which of the following is a possible expansion for this logarithm? Check all that apply.

a)

$\log_34+\log_33$

b)

$\log_310+\log_32$

c)

$\log_32+\log_36$

d)

$\log_336-\log_33$

e)

$\log_315-\log_33$

27.

$\log_324$
Which of the following is a possible expansion for this logarithm? Check all that apply.

a)

$\log_34+\log_320$

b)

$\log_310+\log_314$

c)

$\log_34+\log_36$

d)

$\log_348-\log_32$

e)

$\log_38+\log_33$

28.

$5\log_{9\ }x$

Condense into a single logarithm. Simplify if possible.

a)

$\log45x$

b)

$\log_95x$

c)

$\log_9x^5$

d)

$\log_{ }14x$

29.

$3\log_45$

Condense into a single logarithm. Simplify if possible.

a)

$\log_415$

b)

$\log_4125$

c)

$\log_43^5$

d)

$\log_{ }60$

30.

$\frac{1}{2}\log_{4\ }9$

Condense into a single logarithm. Simplify if possible.

a)

$\log18$

b)

$\log_4\ \frac{9}{2}$

c)

$\log_44.5$

d)

$\log_43$

31.

$\log_{3\ }4^8$

Expand using the product property. Simplify if possible.

a)

$8\log_34$

b)

$4\log_38$

c)

$3\log_84$

d)

$8\log_43$

32.

Condense this expression into a single logarithm.

a)

b)

c)

d)

33.

Write the logarithm expression as a single logarithm

2log 4 + log 2

a)

log 8

b)

log 16

c)

log 32

d)

log 8²

34.

Write as one logarithm. Simplify, if possible.

log₃9 + log₃27

a)

log₃3

b)

log₃243

c)

log₃1/3

d)

not possible

35.

Expand the logarithm expression

log 6x³y

a)

log 6x³ + log y

b)

log 6 + log x³ + log y

c)

3 log 6 + log x + log y

d)

log 6 + 3log x + log y

36.

Expand the logarithm expression

log 5x/4y

a)

log 5x + log 4y

b)

log 5x - 4log y

c)

(log 5 + log x) - (log 4 + logy)

d)

5log x - 4 logy

37.

Write as one logarithm. Simplify, if possible.

(log 3 - log 6) + log 2

a)

log 4

b)

log 2

c)

log 1

d)

log 6

38.

Expand the logarithm expression

log₅5x^-5

a)

-5(log₅5x)

b)

-5log₅5 + log₅x

c)

log₅25x

d)

log₅5 - 5log₅x

39.

$\log_36+\log_3x=\log_312$

a)

$\frac{1}{2}$

b)

$6$

c)

$2$

d)

$4$

40.

$\log_4x+\log_48=\log_424$

a)

$3$

b)

$\frac{1}{3}$

c)

$2$

d)

$4$

41.

$\log18-\log3x=\log2$

a)

$\frac{1}{3}$

b)

$\frac{1}{2}$

c)

$4$

d)

$3$

42.

$\log_7100-\log_7\left(x+5\right)=\log_710$

a)

$2$

b)

$4$

c)

$5$

d)

$10$

43.

$\log x+\log\left(x+9\right)=1$

a)

$1$

b)

$10$

c)

$-10$

d)

$-1$

44.

$\log_2\left(15x-15\right)-\log_2\left(-x^2+1\right)=1$

a)

all real numbers

b)

$\frac{17}{2}$

c)

$-\frac{17}{2}$

d)

no real solution

45.

$\log_4\left(2x+2\right)-\log_4\left(x-2\right)=1$

a)

$\frac{1}{2}$

b)

$2$

c)

$5$

d)

no real solution

solve Logarithmic equations

Total questions: 45

Worksheet time: 3hrs 1mins

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