Log Properties

Use the property Log_b(xy) = Log_b(x) + Log_b(y)

to expand: Log₃(5x)

• $\log_2\left(5\right)\ \times\ \log_2\left(x\right)$

• $\log_2\left(5\right)\ +\ \log_2\left(x\right)$

• $\log_2\left(5\right)\ -\ \log_2\left(x\right)$

• $\log_2\left(5\ +\ x\right)\$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Use the property  $\log_b\left(\frac{x}{y}\right)\ =\ \log_b\left(x\right)\ -\ \log_b\left(y\right)$  
to expand  $\log_2\left(\frac{x}{4}\right)\$  

•  $\log_2\left(x\right)\ \times\ \log_2\left(4\right)$ 

•  $\log_2\left(x\right)\ +\ \log_2\left(4\right)$ 

•  $\log_2\left(x\right)\ -\ \log_2\left(4\right)$ 

•  $\log_2\left(5\right)\ -\ \log_2\left(x\right)\$ 

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Use the property  $\log_b\left(x\right)^a\ =\ a\log_b\left(x\right)\$  
to expand  $\log_5\left(x\right)^2\$  

•  $5\log_2\left(x\right)\$ 

•  $2\log_5\left(x\right)\$ 

•  $\log_5\left(x\right)\ +\ \log_5\left(2\right)$ 

•  $\log_5\left(x\right)\ -\ \log_5\left(2\right)\$ 

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Use the change of base property  $\log_b\left(x\right)\ =\ \frac{\log_a\left(x\right)}{\log_a\left(b\right)}\$  
to write  $\log_2\left(16\right)\$  with the common base

•  $\log\left(8\right)$ 

•  $\frac{\log\left(16\right)}{\log\left(2\right)}$ 

•  $\frac{\log\left(2\right)}{\log\left(16\right)}$ 

•  $\log\left(16\right)\ +\ \log\left(2\right)\$ 

Tags

CCSS.HSF.BF.B.5

Expand  $\log_4\left(6y\right)$  

•  $\log_4\left(6\right)\ +\ \log_4\left(y\right)$ 

•  $\log_4\left(6\right)\ -\ \log_4\left(y\right)$ 

•  $y\log_4\left(6\right)\$ 

•  $\log_4\left(\frac{6}{y}\right)\$ 

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand  $\log_4\left(3xy\right)$  

•  $\log_4\left(3\right)\ +\ \log_4\left(x\right)-\ \log_4\left(y\right)$ 

•  $3\log_4\left(x\right)\ +\ 3\log_4\left(y\right)$ 

•  $\log_4\left(3\right)\ +\ \log_4\left(x\right)+\ \log_4\left(y\right)\$ 

•  $4\log\left(3\right)\ +\ 4\log\left(x\right)+\ 4\log\left(y\right)\$ 

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand  $\log_2\left(3y^2\right)$  

•  $\log_2\left(3\right)\ +\ \log_2\left(y\right)$ 

•  $2\log_2\left(3\right)\ +\ 2\log_2\left(y\right)$ 

•  $\log_2\left(3\right)\ +\ 2\log_2\left(y\right)$ 

•  $\log_2\left(\frac{3}{y^2}\right)\$ 

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Expand  $\log_2\left(\frac{x}{3y}\right)$  

•  $\log_2\left(x\right)\ +\ \log_2\left(3\right)\ +\ \log_2\left(y\right)$ 

•  $3\log_2\left(x\right)\ +\ \log_2\left(y\right)$ 

•  $\log_2\left(x\right)\ -\ 3\log_2\left(y\right)$ 

•  $\log_2\left(x\right)\ -\ \log_2\left(3\right)\ -\ \log_2\left(y\right)$ 

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Use change of base property to write  $\frac{\log16}{\log3}$  as one Log

•  $\log_3\left(16\right)\$ 

•  $\log_{16}\left(3\right)$ 

•  $\log\left(13\right)$ 

•  $\log\left(19\right)$ 

Tags

CCSS.HSF.BF.B.5

Use properties of Logs to write  $\log_3\left(6\right)+\log_3\left(2\right)$  

as one Log

•  $\log_3\left(8\right)\$ 

•  $\log_3\left(4\right)$ 

•  $\log_3\left(12\right)$ 

•  $\log_3\left(3\right)$ 

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8