Free Printable Properties of Logarithmic Functions

1.

log (4x)

a)

log (4)-log (x)

b)

log (4)+ log (x)

c)

4 log (x)

d)

x log (4)

2.

log (xy²)

a)

log (x)+2 log (y)

b)

log (x)+log (y²)

c)

log (x) - 2 log (y)

d)

log (x) + log (y) + log (2)

3.

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

a)

log (x) + log (y)

b)

x log (y)

c)

log (x-y)

d)

log (x) - log (y)

4.

Expand $\log_4\left(6y\right)$

a)

$\log_4\left(6\right)\ +\ \log_4\left(y\right)$

b)

$\log_4\left(6\right)\ -\ \log_4\left(y\right)$

c)

$y\log_4\left(6\right)\$

d)

$\log_4\left(\frac{6}{y}\right)\$

5.

Use properties of Logs to write $\log_3\left(6\right)+\log_3\left(2\right)$

as one Log

a)

$\log_3\left(8\right)\$

b)

$\log_3\left(4\right)$

c)

$\log_3\left(12\right)$

d)

$\log_3\left(3\right)$

6.

Condense:

$\log_2\left(6\right)+\log_2\left(3\right)$

a)

log₂(18)

b)

log₂ (2) = 1

c)

log₂ (3)

d)

log₂ (9)

7.

Condense: log (16) + log (2) - log (8)

a)

log (4)

b)

log (8)

c)

log (10)

d)

log (24)

8.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

9.

Expand completely: log(2x⁵)

a)

log 2 + 5log x

b)

5log 2 + 5log x

c)

5log 2 + log x

d)

log 10 + log x

10.

Use multiple log properties to write as a single log:
3log₂x - log₂y + log₂z

a)

log₂(x/(yz))

b)

log₂(x³yz)

c)

log₂(x³z/y)

d)

log₂(x³/(yz))

Properties of Logarithmic Functions

Total questions: 10

Worksheet time: 20mins

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