PROPERTIES OF LOGARITHMS BLOCK 2 HONS

7.4 - Properties of Logarithms

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Let's recap what you learned:

More:

Inverse Property of Logarithms and Exponents

Change of Base Formula

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):  $\log_5100\ -\ 2\log_52$  

Fill in the Blank

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 Blank

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

log₈8

• 8
• -8
• 1
• 0

Multiple Choice

How many times as much energy is released by a magnitude-8.5 earthquake as a magnitude-6.5 earthquake?

(E=10^(1.5M+11.8))

• 1000

• 100

• 2

• 10000

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.
 $\log\frac{x}{y^6}$  

•  $\log x+6\log y$  
  

•  $\log x-6\log y$  
  

•  $\log x+\log6y$  
  

•  $\log x-\log6y$