Free Printable 6-5 Properties of Logarithms

1.

Condense: $3\ln x\ +\ 8\ln y$

a)

$\ln\left(\frac{x^3}{y^8}\right)$

b)

$\ln\left(x^3y^8\right)$

c)

$24\ln\left(xy\right)$

d)

$11\ln\left(xy\right)$

2.

Expand $\log_3\ \left(\frac{x^2}{y}\right)$

a)

$\log_3\ y\ +\log_3\ x^2$

b)

$\log_3\ x\ +\log_3\ 2\ -\ \log_3\ y\$

c)

$2\log_3\ x\ -\log_3\ y$

d)

$2\log_3\ xy$

3.

Expand $\log_2\ \left(\frac{2x}{p^5}\right)$ completely.

a)

$\log_2\ x\ -\ \log_2\ p$

b)

$1\ +\log_2x\ -5\ \log_2\ p$

c)

$\log_2\ 2\ -\ \log_2\ x\ +\log_2\ p^5$

d)

$\log_2\ 2x\ +\ \log_2\ p^5$

4.

Which of the following is equivalent to $\log_b(x^n)$ ?

a)

$\log_b\left(xn\right)$

b)

$\left(\log_b\left(x\right)\right)^n$

c)

$x^n\cdot\log_b\left(x\right)$

d)

$n\cdot\log_b\left(x\right)$

5.

Condense $\log\ \left(2\right)\ +\ \log\ \left(5\right)$

(a)

6.

Condense $\log\ \left(20\right)\ -\ \log\ \left(5\right)$

(a)

7.

$2\ \log\ 10$

(a)

8.

Condense $3\ \ln\ 2\ +\ln\ z$

(a)

9.

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

a)

$\log_4\ x\ -\ \log_4\ y$

b)

$\log_4\ x\ +\ \log_4\ y$

c)

$2\log_4\ x\ -\ 2\log_4\ y$

d)

$2\log_4\ x\ +\ 2\log_4\ y$

10.

$5\ \log_2\ c-5\ \log_2\ n$

a)

$\log_2\ \left(\frac{c}{n}\right)^5$

b)

$0$

c)

$\log_2\ \left(cn\right)^5$

d)

$\log\ \frac{c}{n}$

6-5 Properties of Logarithms

Total questions: 10

Worksheet time: 10mins

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