Properties of Logarithms

Expand: $\log_6\left(\frac{5}{4y}\right)$  

•  $\log_65\ +\ \log_64\ +\ \log_6y$  

•  $\log_65\ -\ \log_64\ +\ \log_6y$  

•  $\log_65\ -\ \log_64\ -\ \log_6y$  

•  $\log_65\ -\ \log_64y$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Condense:  $\log\left(5x+2\right)\ -\ \log3\ -\ \log x$  

•  $\log\left(\frac{3x}{5x\ +\ 2}\right)$  

•  $\log\left(\frac{5x\ +\ 2}{3x}\right)$  

•  $\log\left(3x\left(5x+2\right)\right)$  

•  $\log\left(\frac{5x\ +\ 2}{3\ -\ x}\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Expand:  $\log_4\left(3x^2\right)$  

•  $2\log_43x$  

•  $2\log_43\ +\ 2\log_4x$  

•  $\log_43\ +\ 2\log_4x$  
  

•  $2\log_43\ +\ \log_4x$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand:

• $\frac{1}{3}\left(2\log_5x\ +\ 3\log_5y\ -\ 5\log_5z\right)$

• $\frac{1}{3}\left(2\log_5x\ -\ 3\log_5y\ -\ 5\log_5z\right)$

• $\frac{1}{3}\left(2\log_5x\ +\ 3\log_5y\ +\ 5\log_5z\right)$

• $2\log_5x\ +\ 3\log_5y\ -\ 5\log_5z$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Condense:  $3\ln x\ +\ 8\ln y$ 

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

•  $\ln\left(x^3y^8\right)$  

•  $24\ln\left(xy\right)$  

•  $11\ln\left(xy\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Condense:  $3\log_bx\ -\ \log_by\ -\ 5\log_bz$ 

•  $\log_b\ \frac{x}{yz^5}$  

•  $\log_b\ \frac{x^3}{yz^{ }}$  

•  $\log\frac{x}{yz^5}$  

•  $\log_b\ \frac{x^3}{yz^5}$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

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

Tags

CCSS.HSF.BF.B.5

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

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Evaluate using properties of logarithms (no calculator):  $\log2\ +\ \log10\ +\ \log5$  

Tags

CCSS.HSF.BF.B.5