Free Printable Condense and expand logarithms

1.

You will have 3 attempts to this assignment. Please watch video lesson before continuing and have your notes available. If you do not do well on the first attempt, study the flash cards and try again. If you still did not do well rewatch the video lesson, and try again.

a)

I am ready to proceed

b)

...

c)

..

d)

.

2.

Which value is equivalent: $\log_21$ ?

a)

0

b)

1

c)

2

d)

$\frac{1}{2}$

3.

Simplify the expression: $\log_66$ ?

a)

0

b)

1

c)

6

d)

36

4.

Which value is equivalent to $\log_{11}\sqrt{11}$ ?

a)

0

b)

1

c)

2

d)

$\frac{1}{2}$

5.

Condense the following expression into a single logarithm: $\log_58+\log_52$

a)

$\log_54$

b)

$\log_56$

c)

$\log_510$

d)

$\log_516$

6.

$\log_224-\log_36$ Condense the following expression into a single logarithm:

a)

$\log_34$

b)

$\log_318$

c)

$\log_330$

d)

$\log_3144$

7.

Condense the expression $10\log_3x+6\log_3y$
into a single logarithm.

a)

$\log_3\left(x^{10}y^6\right)$

b)

$\log_3\left(x^{10}+y^6\right)$

c)

$\log_3\left(\frac{x^{10}}{y^6}\right)$

d)

$\log_3\left(xy\right)^{16}$

8.

Which expression is equivalent to $\log_2\left(\frac{m^4}{n^7}\right)$

a)

$4\log_2m+7\log_2m$

b)

$7\log_2m+4\log_2m$

c)

$4\log_2m-7\log_2m$

d)

$7\log_2m-4\log_2m$

9.

Which expression is equivalent to:

$\frac{1}{2}\ln\left(a\right)+\frac{1}{2}\ln\left(b\right)$

a)

$\ln\left(ab\right)^2$

b)

$\ln\left(ab^{\frac{1}{2}}\right)$

c)

$\ln\left(\sqrt{ab}\right)$

d)

$\ln\left(a^{\frac{1}{2}}b\right)$

10.

Expand the expression:
$\log_8\left(7x^4\right)$

a)

$\log_87+4\log_8x$

b)

$\log_87-4\log_8x$

c)

$4\log_87+4\log_8x$

d)

$4\log_87-4\log_8x$

11.

Condense the following expression into a single logarithm:
$2\log\left(a\right)+4\log\left(b\right)-9\log\left(c\right)$

a)

$\log\left(a^2b^4c^9\right)$

b)

$\log\left(a^2+b^4-c^9\right)$

c)

$\log\left(\frac{a^2b^4}{c^9}\right)$

d)

$\log\left(\frac{a^2}{b^4c^9}\right)$

Condense and expand logarithms

Total questions: 11

Worksheet time: 21mins

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