Free Printable Log Practice

1.

log₂32=3x

a)

5/3

b)

3/5

c)

5

d)

3

2.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

3.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

4.

log₈₁x = 3/4

a)

2

b)

3

c)

27

d)

81

5.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

6.

Change to Logarithmic Form:
5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

7.

lnx = -3

a)

8.1548

b)

-8.1548

c)

0.0498

d)

-0.0498

8.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

9.

Find the time required for an investment of $1000 to grow to $5000 at an interest rate of 8% per year compounded monthly. (round to nearest year)

a)

1 year

b)

242 years

c)

20 years

d)

13 years

10.

June bugs are tripling in number each week. If there are currently 300 June Bugs in the backyard, when will there be 8100 June Bugs?

a)

2 weeks

b)

3 weeks

c)

300 weeks

d)

27 weeks

11.

Which of the following expressions is equivalent to $6\log\left(x\right)-2\log\left(y\right)?$

SHOW WORK!

a)

$\log\left(x^6+y^2\right)$

b)

$\log\left(\frac{6x}{2y}\right)$

c)

$\log\left(\frac{x^6}{y^2}\right)$

d)

$\log\left(x^6\cdot y^2\right)$

12.

Solve the following equation for x: $\log_5\left(x+13\right)=2$

SHOW WORK!

a)

$x=12$

b)

$x=38$

c)

$x=19$

d)

$x=-3$

13.

Write the exponential equation as a logarithm
6³=216

a)

log₆(3) = 216

b)

log₃(6) = 216

c)

log₆(216)=3

d)

log₂₁₆(6)=3

14.

Write in exponential form.

\log_2\left(\frac{1}{8}\right)=-3

a)

$2^{-3}=\frac{1}{8}$

b)

$2^{\frac{1}{8}}=-3$

c)

$-3^2=\frac{1}{8}$

d)

$-3^{\frac{1}{8}}=2$

15.

Expand the logarithmic expression.

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

a)

$\ln\left(2\right)+2\ln\left(x\right)-\ln\left(y\right)+4\ln\left(z\right)$

b)

$\ln\left(2\right)+\ln\left(x\right)^2+\ln\left(y\right)-\ln\left(z\right)^4$

c)

$\ln\left(2\right)+\ln\left(x\right)+\ln\left(y\right)-4\ln\left(z\right)$

d)

$\ln\left(2\right)+2\ln\left(x\right)+\ln\left(y\right)-4\ln\left(z\right)$

16.

Rewrite e^x = 9 using a natural logarithm.

a)

ln x = 9

b)

ln 9 = x

c)

log_x e = 9

d)

log₉ x = e

17.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

18.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

19.

Write in logarithmic form.
2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

20.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

21.

log₄1 =

a)

0

b)

1

c)

4

d)

DNE

22.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

23.

Write the following equation in logarithmic form:
3⁵ = 243

a)

log₃5 = 243

b)

log₂₄₃3 = 5

c)

log₅243 = 3

d)

log₃243 = 5

Log Practice

Total questions: 23

Worksheet time: 3hrs 54mins

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