Free Printable Logarithmic Functions

1.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

2.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

3.

Simplify: log(3) + 2log(5)

a)

log(75)

b)

2log(15)

c)

log(30)

d)

log(13)

4.

Rewrite with no coefficient:

3\log_23

a)

$\log_29$

b)

$\log_21$

c)

$\log_227$

d)

$\log_26$

5.

Condense into a single log:

2\log7+5\log x-2\log5

a)

$\log\left(\frac{49x^5}{25}\right)$

b)

$\log\left(\frac{49x^5}{10}\right)$

c)

$\log\left(\frac{14x^5}{25}\right)$

d)

$\log\left(\frac{14x^5}{10}\right)$

6.

Solve for x:

\log_x\sqrt{6}=\frac{1}{2}

*Hint: Rewrite as an exponential first.

(a)

7.

Use the change of base rule to rewrite this problem:

log₃64

a)

log(64)/log(3)

b)

log(3)/log(64)

8.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

9.

What is the value of "e"?

a)

1

b)

3.1416

c)

2.718...

d)

Does not exist

10.

Simplify $2\cdot\ln e^5$

a)

2

b)

5

c)

10

d)

10 ln e

11.

33 = x^y

a)

log ₃₃y = x

b)

log _x 33 = y

c)

log _y 33 = x

d)

log _x y = 33

12.

$3^{2x}=27$ Solve for x.

a)

2

b)

3

c)

1.5

d)

1

13.

$Expand\ the\ \log$

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

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

14.

$\log0,0001\ =....$

a)

4

b)

-4

c)

3

d)

-3

e)

0

15.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

16.

What are the transformations of this graph?

a)

Right 1 Up 5

b)

Right 1 Down 5

c)

Left 1 Up 5

d)

Left 1 Down 5

17.

What is the Range?

a)

y > 0

b)

All Real Numbers

c)

y > 1

d)

y < 1

18.

log_a x

This function always passes thru coordinate:

a)

(0, 1)

b)

(1, 0)

c)

(0, a)

d)

(a, 0)

19.

Find the corresponding graph of
$\log_3\left(x\right)-2$

a)

b)

c)

d)

20.

What is the domain for

g\left(x\right)=\log_2\left(x-3\right)

?

a)

All real numbers

b)

$\left(3,\infty\right)$

c)

$\left(0,\infty\right)$

d)

$\left(-\infty,3\right)$

Logarithmic Functions

Total questions: 20

Worksheet time: 20mins

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