Properties of Logarithms

Write log_b(xy) as two logs

• log_bx+log_by
• log_bx-log_by
• log_bx*log_by
• log_bx/log_by

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Write log_b(x/y) as two logs

• log_bx-log_by
• log_bx+log_by
• log_bx*log_by
• log_bx/log_by

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Rewrite log_b(xⁿ)

• nlog_bx
• (log_bx)ⁿ
• xⁿlog_bx
• log_b(xⁿ)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Which property of logarithms is demonstrated below:


 $\log_920\ =\ \frac{\log20}{\log9}$  

• Product property

• Quotient property
  

• Power property

• Change of Base Property

Use the properties of logarithms to retwrite

• A

• B

• C

• D

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Rewrite as a single logarithm:

 $\log3\ +\ \log7$  

• log 10

• log 21

• log 3/7

• log 3/log 7

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Rewrite as a single logarithm:

 $\log_260\ -\ \log_210$  

•  $\log_26$  
  

•  $\log_250$  
  

•  $\frac{\log_260}{\log_210}$  
  

•  $\log_270$  
  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Use the properties of logarithms to rewrite as the sum of two logarithms:

 $\log55$  

• log 40 + log 15

• log 50 + log 5

• log 11 + log 5

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Use the properties of logarithms to rewrite as the difference of two logs:

 $\log_545$  

•  $\log_590\ -\log_52$  

•  $\log_515-\log_53$  

•  $\frac{\log45}{\log\ 5}$  

•  $\log_550-\log_55$  

Tags

CCSS.HSF.BF.B.5

Which of the logarithms below is equivalent to the following:
 $2\log12$  

• log 10

• log 6

• log 24

• log 144

Tags

CCSS.HSF.BF.B.5