Free Printable Condense and Expand Logs

1.

Condense $15\ \log_5a\ +3\ \log_5b$

a)

$15\log_5ab$

b)

$\log_5\left(a^{15}b^3\right)$

c)

$\log_5\left(b^{15}a^3\right)$

d)

$45\log_5\left(ab\right)$

2.

$4\log_4u-6\log_4v$ Condense

a)

$\log_4\left(\frac{u}{v}\right)^{24}$

b)

$\log_4\left(\frac{u^6}{v^4}\right)^{ }$

c)

$\log_4\left(\frac{u^4}{v^6}\right)^{ }$

d)

$\log_4\left(\frac{v^6}{u^4}\right)^{24}$

3.

Expand $\log_4\left(x^5y^2\right)$

a)

$10\log_4\left(x\ +y\right)$ 1

b)

$5\log_4x+2\log_4y$

c)

$5\log_9x+2\log_9y$

d)

$\log_4\left(5x+2y\right)$

4.

$Expand\ \log_5\left(xy^5\right)^2$

a)

$2\log_5x\ +10\log_5y$

b)

$10\left(\log_5x\ +\log_5y\right)$

c)

$10\log_5x\ +10\log_5y$

d)

$10\log_5x\ +2\log_5y$

5.

Write the log in exponential form
$\log_3y=9$

a)

$3^9=x$

b)

$3^x=9$

c)

$3^9=81$

d)

$x^3=9$

6.

Write the log in exponential form
$\log_5y=2$

a)

$5^y=2$

b)

$2^5=y$

c)

$2^y=5$

d)

$5^2=y$

7.

Write in a log form
$3^5=y$

a)

$\log_3y=15$

b)

$\log_5y=3$

c)

$\log_3y=3$

d)

$\log_3y=5$

8.

Expand the Log completely and simplify if possible. $\log_{ }\left(\frac{\sqrt{x}}{z^5y}\right)$

a)

$\frac{1}{2}\log x\ -5\log z-\log y$

b)

$\log\ x^{\frac{1}{2}\ }-\log\ z^5+\log\ y$

c)

$\log\ \sqrt{x}-\log z^5+y^{ }$

d)

$10\log\ x-z+y$

Condense and Expand Logs

Total questions: 8

Worksheet time: 4mins

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