Free Printable Condense and expand logarithms (quotients and products)

1.

Which of the following illustrates the Product Property of Logarithms

a)

log₃(x) ⋅ log₃(y) = log₃(x+y)

b)

log₃(x) ⋅ log₃(y) = log₃(xy)

c)

log₃(x) + log₃(y) = log₃(xy)

2.

Which of the following illustrates the Quotient Property of Logarithms

a)

log₄(x ÷ y) = log₄(x) - log₄(y)

b)

log₄(x ÷ y) = log₄(x) ÷ log₄(y)

c)

log₄(x - y) = log₄(x) ÷ log₄(y)

3.

Expand the following: $\log_24g$

a)

$\log_24\times\log_2g$

b)

$\log_24+\log_2g$

c)

$\log_24-\log_2g$

d)

$\frac{\log_24}{\log_2g}$

4.

Expand the following: $\log\frac{n}{m}$

a)

$n\log m$

b)

$\log n+\log m$

c)

$\log n-\log m$

d)

$\frac{\log n}{\log m}$

5.

Condense the Logarithm: $\log_4x+\log_4y$

a)

$4\log xy$

b)

$\log_4xy$

c)

$y\log_4x$

d)

$\log_4\ \frac{x}{y}$

6.

Condense the Logarithm: $\log_4x-\log_4y$

a)

$4\log_{ }xy$

b)

$\log_4xy$

c)

$y\log_4x$

d)

$\log_4\ \frac{x}{y}$

7.

Expand the following: $\log_5\left(\frac{4xy}{z}\right)$

a)

$\log_54x+\log_5y-\log_5z$

b)

$\log_54+\log_5x+\log_5y-\log_5z$

c)

$\log_54xy-\log_5z$

d)

$\frac{\log_54xy}{\log_5z}$

8.

Expand the following: $\log_2\frac{x}{6y}$

a)

$\frac{\log_2x}{\log_26y}$

b)

$\log_2x+\log_26y$

c)

$\log_2x-\log_26-\log_2y$

d)

$\log_2x-\log_26+\log_2y$

9.

Write as one logarithm. Simplify, if possible.
log₆3 + log₆2

a)

0

b)

log₆5

c)

log₆1

d)

1

10.

Condense into a single log and simplify

\log_280-\log_25

a)

$\log_275$

b)

$\log_2400$

c)

8

d)

4

Condense and expand logarithms (quotients and products)

Total questions: 10

Worksheet time: 9mins

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