Free Printable Attributes and Properties of Logarithmic Functions

1.

What the equation in logarithmic form?

32\ =\ 2^5

a)

$\log_52\ =\ 32$

b)

$\log_{32}5\ =\ 2$

c)

$\log_232\ =\ 5$

2.

What is the logarithmic form of the equation?

243\ =\ 3^5

a)

$\log_3243\ =\ 5$

b)

$\log_53\ =\ 243$

c)

$\log_{243}3\ =\ 5$

3.

Write the equation in exponential form.

\log_39\ =\ 2

a)

$2^3=9$

b)

$9^2\ =\ 3$

c)

$3^2\ =\ 9$

d)

$9^3=2$

4.

Write the equation in exponential form.

\log_5125\ =\ 3

a)

$3^5=\ 125$

b)

$125^3=\ 5$

c)

$125^{5\ }=\ 3$

d)

$5^3\ =\ 125$

5.

What is the minimum and maximum of the function below given the interval [4, 32]?

f\left(x\right)=\log_2x

a)

Minimum: x = 2, Maximum: x = 5

b)

Minimum: y = 5, Maximum: y = 2

c)

Minimum: y = 2, Maximum: y = 5

d)

Minimum: x = 5, Maximum: x = 2

6.

What is the inverse of

y=\log_8x

?

a)

$8^y=x$

b)

$y^8=x$

c)

$8^x=y$

d)

$x^8=y$

7.

Write the expression as a single logarithm.

\log_39+\log_324

a)

$\log_3\left(\frac{9}{24}\right)$

b)

$\log_39+24$

c)

$\log_324^9$

d)

$\log_39\cdot24$

8.

What is the expression as a single logarithm?

\log_27-\log_29

a)

$\log_27-9$

b)

$\log_2\left(\frac{7}{9}\right)$

c)

$\log_27\cdot9$

d)

$\log_2\left(\frac{9}{7}\right)$

9.

Expand the logarithm.

\log_4y^2z^3

a)

$6\log_4yz$

b)

$2\log_4y\ +\ 3\log_4z$

c)

$2\log_4y-3\log_4z$

d)

$6\log_4y+\log_4z$

10.

Use the Change of Base Formula to evaluate the expression.

\log_927

a)

$\frac{3}{2}$

b)

$\frac{2}{3}$

c)

$\frac{1}{3}$

d)

3

11.

Evaluate the logarithm.

\log_{125}\left(\frac{1}{25}\right)

a)

$\frac{2}{3}$

b)

$\frac{-2}{3}$

c)

$\frac{3}{2}$

d)

$\frac{-3}{2}$

12.

Use the Change of Base Formula to evaluate the expression.

\log_412

a)

$\frac{14}{25}$

b)

$\frac{25}{14}$

c)

$\frac{100}{179}$

d)

$\frac{179}{100}$

Attributes and Properties of Logarithmic Functions

Total questions: 12

Worksheet time: 36mins

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