Free Printable Log Properties

1.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

2.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

3.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

4.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

5.

Condense

a)

A

b)

B

c)

C

d)

D

6.

Expand

a)

A

b)

B

c)

C

d)

D

7.

Condense

a)

A

b)

B

c)

C

d)

D

8.

a)

log₅(x²z²y¹⁰)

b)

log₅(z²y²x¹⁰)

c)

log(zy²x¹⁰)

d)

log₅(z² + y²+ x¹⁰)

9.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

10.

Condense

a)

A

b)

B

c)

C

d)

D

11.

a)

log(x) + log(z) + 4log(y)

b)

3log(x) − log(z) − 4log(y)

c)

3log(x) + log(z) + 4log(y)

d)

log(x) − 4log(z) − 3log(y)

12.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

13.

Use the property Log_b(xy) = Log_b(x) + Log_b(y)

to expand: Log₃(5x)

a)

$\log_2\left(5\right)\ \times\ \log_2\left(x\right)$

b)

$\log_2\left(5\right)\ +\ \log_2\left(x\right)$

c)

$\log_2\left(5\right)\ -\ \log_2\left(x\right)$

d)

$\log_2\left(5\ +\ x\right)\$

14.

Use the property $\log_b\left(\frac{x}{y}\right)\ =\ \log_b\left(x\right)\ -\ \log_b\left(y\right)$
to expand $\log_2\left(\frac{x}{4}\right)\$

a)

$\log_2\left(x\right)\ \times\ \log_2\left(4\right)$

b)

$\log_2\left(x\right)\ +\ \log_2\left(4\right)$

c)

$\log_2\left(x\right)\ -\ \log_2\left(4\right)$

d)

$\log_2\left(5\right)\ -\ \log_2\left(x\right)\$

15.

a)

5log₆(a) + 6log₆(c) − 30log₆(b)

b)

log₆(a) + 6log₆(c) − 5log₆(b)

c)

6log₆(a) − 6log₆(c) − 30log₆(b)

d)

6log₆(a) + 6log₆(c) − 30log₆(b)

16.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

Log Properties

Total questions: 16

Worksheet time: 34mins

Similar Resources on Wayground