Basic Logarithmic Properties

7.4 - Properties of Logarithms

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Objective

To use the properties of logarithms

Recall:

More:

Inverse Property of Logarithms and Exponents

Change of Base Formula

Practice next:

Multiple Choice

Condense into a single logarithm. Evaluate if possible. $$\log\ 25\ +\ \log\ 4$$

• $$\log\ 29$$

• $$\log\ 100\ =\ 2$$

• $$\log\ 21$$

• Cannot be condensed

Fill in the Blanks

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

Fill in the Blanks

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

Multiple Choice

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

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

• $$\ln\left(x^3y^8\right)$$  

• $$24\ln\left(xy\right)$$  

• $$11\ln\left(xy\right)$$  

Fill in the Blanks

Evaluate using Change of Base Formula: $\log_45$ Round to the nearest hundredth.

Multiple Choice

The common logarithm has what base?

• 10

• 0

• e

• -e

Multiple Choice

Evaluate: 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

Poll

Select the image that best reflects how well you feel you can use the properties of logarithms:

• Mr. Dull, that's the worst geography pun I ever saw