Properties of Logarithms

Properties of Logarithms

Let's recap what you learned:

More:

Inverse Property of Logarithms and Exponents

Practice next:

Multiple Choice

• log(x) + log(z) + 4log(y)

• 3log(x) − log(z) − 4log(y)

• 3log(x) + log(z) + 4log(y)

• log(x) − 4log(z) − 3log(y)

Fill in the Blank

Evaluate using properties of logarithms (no calculator): $$\log_5100\ -\ 2\log_52$$  

(simplify completely!)

Fill in the Blank

Evaluate using properties of logarithms (no calculator): $$\log_64\ +\ \log_654$$  

(simplify completely!)

Multiple Choice

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

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

• $$\ln\left(x^3y^8\right)$$  

• $$24\ln\left(xy\right)$$  

• $$11\ln\left(xy\right)$$  

Multiple Choice

The common logarithm has what base?

• 10

• 0

• e

• -e

Multiple Choice

log₈8

• 8
• -8
• 1
• 0

Multiple Choice

Simplify.

10^log125

• 125

• 12.5

• 1250

• log125

Multiple Choice

Express as a single logarithm.

Log₆9 + Log₆24

• Log₆216 = 3

• Log₆33 ≈ 1.95

• Log₆(8/3) ≈ 1.16

• Log₆216 = 36

Multiple Choice

Condense each expression to a single logarithm. $$\log_4u-6\log_4v$$  

• $$\log_4\frac{v^6}{u}$$

• $$\log_4\frac{u}{v^6}$$  

• $$\log_4\left(uv\right)^6$$  

• $$\log_4\left(u\cdot v^6\right)^{ }$$  

Multiple Choice

Condense each expression to a single logarithm. $$\log7-2\log12$$  

• $$\log\frac{7}{24}$$  

• $$\log\frac{7}{144}$$  

• $$2\log\frac{7}{12}$$  

• $$\log\frac{49}{144}$$  

Multiple Choice

Expand the logarithm. $$\log\frac{x}{y^6}$$  

• $$\log x+6\log y$$  

• $$\log x-6\log y$$  

• $$\log x+\log6y$$  

• $$\log x-\log6y$$