Properties of Logs

Condense into a single logarithm.
 $\ln7-\ln2$  

• ln 5

• ln 14

•  $\ln\frac{2}{7}$   
  

•  $\ln\frac{7}{2}$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Condense into a single logarithm.
 $\log_25+\log_29+\log_2w$  

•  $\log_2\left(14w\right)$  
  

•  $\log_2\left(45w\right)$  
  

•  $\log_2\left(\frac{14}{w}\right)$   
  

•  $\log_2\left(14+w\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Condense into a single logarithm.
 $\log_43+2\log_4x+3\log_4y$  

•  $\log_4\left(3x^2y^3\right)$  
  

•  $\log_4\left(18xy\right)$  
  

•  $\log_4\left(3xy\right)$   
  

•  $\log_4\left(8xy\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Condense into a single logarithm.
 $4\log_7x-3\log_7y$  

•  $\log_7\left(x^{12}y^3\right)$  
  

•  $\log_7\left(12xy\right)$  
  

•  $\log_7\left(\frac{x^4}{y^3}\right)$   
  

•  $\log_4\left(\frac{4x}{3y}\right)$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Condense into a single logarithm.
 $2\ln m+2\ln p-\ln9$  

•  $\ln\left(\frac{4mp}{9}\right)$  
  

•  $\ln\left(\frac{m^2p^2}{9}\right)$  
  

•  $\ln\left(36mp\right)$   
  

•  $\ln\left(m^2p^2-9\right)$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSF.LE.A.4

Condense into a single logarithm.
 $2\log_5x+2\log_5z+10\log_5y$  

•  $\log_5\left(14xyz\right)$  
  

•  $\log_5\left(40xyz\right)$  
  

•  $\log_5\left(x^2y^{10}z^2\right)$   
  

•  $\log_5\left(xz^2y^{10}\right)$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Expand into multiple logarithms.   $\log_3\left(a^2b^3\right)$  

•  $\log_3\left(2a\right)+\log_3\left(3b\right)$  

•  $\frac{\log_3\left(2a\right)}{\log_3\left(3b\right)}$  

•  $2\log_3a-3\log_3b$  

•  $2\log_3a+3\log_3b$  

Expand into multiple logarithms.   $\ln\left(\frac{6}{m^4}\right)$  

•  $\ln6-\ln\left(4m\right)$  

•  $\ln6+\ln\left(4m\right)$  

•  $\ln6-4\ln m$  

•  $\ln6-4\ln\left(\frac{1}{m}\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand into multiple logarithms.   $\log\left(xyz^3\right)$  

•  $\log x+\log y+3\log z$  

•  $3\log x+3\log y+3\log z$  

•  $\log x-\log y-3\log z$  

•  $\left(\log x\right)\left(\log y\right)\left(3\log z\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Expand into multiple logarithms.   $\log_5\frac{a^4b}{c^7}$  

•  $\log_5\left(4a\right)+\log_5b-\log_5\left(7c\right)$  

•  $4\log_5a+\log_5b-7\log_5c$  

•  $\log x-\log y-3\log z$  

•  $\left(\log x\right)\left(\log y\right)\left(3\log z\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5