Free Printable 5.3 Properties of Logs

1.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

2.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

3.

$\log\left(\frac{x}{y}\right)$

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

4.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

5.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

6.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

7.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

8.

a)

ln(wvu⁵)

b)

ln(u + v + w⁵)

c)

ln(uvw⁵)

d)

ln(uvw)⁵

9.

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)

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

10.

$4\log_4u-6\log_4v$ 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)

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

11.

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)

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

12.

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

a)

$2\log_5x\ +10\log_5y$

b)

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

c)

$10\log_5x\ +10\log_5y$

d)

$10\log_5x\ +2\log_5y$

13.

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

a)

$3^9=x$

b)

$3^x=9$

c)

$3^9=81$

d)

$x^3=9$

14.

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

a)

$5^y=2$

b)

$2^5=y$

c)

$2^y=5$

d)

$5^2=y$

15.

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

a)

$\log_3y=15$

b)

$\log_5y=3$

c)

$\log_3y=3$

d)

$\log_3y=5$

16.

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)

$10\log\ x-z+y$

17.

What would the change base look like for:

log₆ 48

a)

log 8

b)

$\frac{\log6}{\log48}$

c)

$\frac{\log48}{\log6}$

d)

ln 8

18.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

19.

Use change of base property to write $\frac{\log16}{\log3}$ as one Log

a)

$\log_3\left(16\right)\$

b)

$\log_{16}\left(3\right)$

c)

$\log\left(13\right)$

d)

$\log\left(19\right)$

20.

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)\$

21.

Use the change of base property $\log_b\left(x\right)\ =\ \frac{\log_a\left(x\right)}{\log_a\left(b\right)}\$
to write $\log_2\left(16\right)\$ with the common base

a)

$\log\left(8\right)$

b)

$\frac{\log\left(16\right)}{\log\left(2\right)}$

c)

$\frac{\log\left(2\right)}{\log\left(16\right)}$

d)

$\log\left(16\right)\ +\ \log\left(2\right)\$

22.

Expand $\log_4\left(6y\right)$

a)

$\log_4\left(6\right)\ +\ \log_4\left(y\right)$

b)

$\log_4\left(6\right)\ -\ \log_4\left(y\right)$

c)

$y\log_4\left(6\right)\$

d)

$\log_4\left(\frac{6}{y}\right)\$

23.

Expand $\log_4\left(3xy\right)$

a)

$\log_4\left(3\right)\ +\ \log_4\left(x\right)-\ \log_4\left(y\right)$

b)

$3\log_4\left(x\right)\ +\ 3\log_4\left(y\right)$

c)

$\log_4\left(3\right)\ +\ \log_4\left(x\right)+\ \log_4\left(y\right)\$

d)

$4\log\left(3\right)\ +\ 4\log\left(x\right)+\ 4\log\left(y\right)\$

24.

Expand $\log_2\left(3y^2\right)$

a)

$\log_2\left(3\right)\ +\ \log_2\left(y\right)$

b)

$2\log_2\left(3\right)\ +\ 2\log_2\left(y\right)$

c)

$\log_2\left(3\right)\ +\ 2\log_2\left(y\right)$

d)

$\log_2\left(\frac{3}{y^2}\right)\$

25.

Expand $\log_2\left(\frac{x}{3y}\right)$

a)

$\log_2\left(x\right)\ +\ \log_2\left(3\right)\ +\ \log_2\left(y\right)$

b)

$3\log_2\left(x\right)\ +\ \log_2\left(y\right)$

c)

$\log_2\left(x\right)\ -\ 3\log_2\left(y\right)$

d)

$\log_2\left(x\right)\ -\ \log_2\left(3\right)\ -\ \log_2\left(y\right)$

26.

Use properties of Logs to write $\log_3\left(4\right)-\log_3\left(x\right)+\log_3\left(y\right)$

as one Log

a)

$\log_3\left(\frac{4x}{y}\right)\$

b)

$\log_3\left(4xy\right)$

c)

$\log_3\left(\frac{4}{xy}\right)$

d)

$\log_3\left(\frac{4y}{x}\right)$

27.

Rewrite as an exponential: $\log_7\left(\frac{1}{49}\right)=-2$

a)

$7^{\frac{1}{49}}=-2$

b)

$\left(\frac{1}{49}\right)^{-2}=7$

c)

$7^{-2}=\frac{1}{49}$

d)

$\left(-2\right)^7=\frac{1}{49}$

28.

Expand: $\log_9\sqrt{23}$

a)

$\frac{1}{2}\log_923$

b)

$\log_9\left(\frac{1}{2}\right)-\log_923$

c)

$\log_9\sqrt{2}+\log_9\sqrt{3}$

d)

$\log_9\ \left(\frac{1}{2}\right)+\log_923$

29.

What it the transformation?

a)

Vertical Translation up 5

b)

Vertical Translation down 5

c)

Horizontal Translation left 5

d)

Horizontal Translation right 5

30.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

5.3 Properties of Logs

Total questions: 30

Worksheet time: 49mins

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