Free Printable LOGARITHMS TEST

1.

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)

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

2.

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)

$x=-3$

3.

Solve for x: $\log_5\left(x+2\right)=\log_5\left(3x+5\right)$

SHOW WORK!

a)

$x=\frac{3}{2}$

b)

$x=-\frac{3}{2}$

c)

$x=\frac{7}{2}$

d)

$x=-\frac{3}{4}$

4.

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

5.

Evaluate.

3 log₂4

a)

3

b)

6

c)

2

d)

4

6.

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)

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

7.

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)

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

8.

What is the base of the following expression?

log(1000) = 3

a)

10

b)

2

c)

e

d)

3

9.

Use the change of base formula to evaluate log₃5.

Round to the nearest thousandth.

a)

-1.465

b)

1.464

c)

.6790

d)

1.465

10.

Which of the following would you use to evaluate log₆17 ?

a)

log(17/6)

b)

log(6/17)

c)

log17/log6

d)

log6/log17

11.

Expand log_x(MN)

a)

xlog(MN)

b)

log_x(M) + log_x(N)

c)

log(N) + log(M)

d)

log_x(M) - log_x(N)

12.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

13.

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

14.

$Solve\ for\ x.\ -3e^{\left(2x+3\right)}+16=1$

SHOW WORK!

a)

x = -0.596

b)

x = -0.965

c)

x = -0.956

d)

x = -0.695

15.

Solve for x and show your work!

2⋅4^{3x – 6}– 8 = 120

a)

x = 3

b)

x = 4

c)

x = 2.9

d)

x = 8

16.

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

17.

Solve the following equation for x. Round your solution to two decimal places.

ln(3x) + ln(2x) = 3 (Definitely a bit tricky, but manageable!)

a)

x = 12.91

b)

x = 4.02

c)

x = 3.35

d)

x = 1.83

18.

Solve for x and CHECK IT!

log₈(x) + log₈(x + 2) = 1

a)

x = -4 & x = 2

b)

x = -4

c)

x = 2

d)

x = -2 & x = 4

19.

Evaluate.

log₆(¹/₂₁₆) = x

a)

x = 3

b)

x = ¹/₃

c)

x = -¹/₃

d)

x = -3

20.

Expand.

a)

$\frac{1}{3}\log\left(x\right)+\log\left(y\right)+\log\left(z\right)$

b)

\frac{\log\left(x\right)}{3}+\frac{\log\left(y\right)}{3}+\frac{\log\left(z\right)}{3}

c)

$\frac{\log\left(x\right)}{3}-\frac{\log\left(y\right)}{3}-\frac{\log\left(z\right)}{3}$

d)

$3\log x+3\log y+3\log z$

21.

Evaluate log_b(b) = _____

a)

-1

b)

0

c)

1

d)

b

22.

$Condense:\ \frac{\ln3}{2}+\frac{\ln11}{2}+\frac{\ln10}{2}$

a)

$\ln\sqrt{330}$

b)

$2\ln\left(330\right)^{\frac{1}{2}}$

c)

$\frac{1}{2}\ln\left(3\cdot11\cdot10\right)$

d)

$2\ln\sqrt{3}\sqrt{11}\sqrt{10}$

23.

Continue solving for x. Which is the correct "step 2"?

a)

$64=x^3$

b)

$64^3=x$

c)

$x^{64}=3$

d)

$3^{64}=x$

24.

$4\log_2\left(2x+24\right)-17=-9$
Once you have isolated the log in the equation, what would be the next step?

a)

log both sides

b)

rewrite as an exponential

c)

nothing, you would not be able to solve it

d)

divide both sides by 2

25.

Evaluate

log₂(¹/₈) = x

a)

x = -3

b)

x = 3

c)

x = -1/3

d)

x = 1/3

LOGARITHMS TEST

Total questions: 25

Worksheet time: 3570secs

Similar Resources on Wayground