Log Properties Practice

log(4x)

• log4-logx

• log4+logx

• 4logx

• xlog4

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

log(xy²)

• logx+2logy

• logx+logy²

• logx-2logy

• logx+logy+log2

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

 $\log\left(\frac{x}{y}\right)$  

• logx+logy

• xlogy

• log(x-y)

• logx-logy

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSF.LE.A.4

 $\log\left(\frac{m^3}{n}\right)$  

• logm-log3-logn

• 3logm+logn

• 3logm-logn

• 3log(m-n)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

log(3x)²

• 2log(3+x)

• 2log3+logx

• log3+2logx

• 2(log3+logx)

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

 $\ln\left(\frac{2x^2y}{z^4}\right)$  

• ln2+2lnx+lny+4lnz

• ln2+2lnx+lny-4lnz

• 2ln(2xy)-4lnz

• 2ln2x+lny-4lnz

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSF.LE.A.4

Condense: log16 + log2 - log8

• log4
• log8
• log10
• log24

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)
• log₂(xy⁵)
• log₂(x/y)⁵
• log₂(x/5y)

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand:
 $\ln\sqrt{r^8s^5}$  

•  $\ln r^4s^{\frac{5}{2}}$  

•  $\ln r^8+\ln s^{\frac{5}{2}}$  

•  $4\cdot\ln r+\frac{5}{2}\ln s$  

•  $4\cdot\ln r-\frac{5}{2}\ln s$  

Condense:  $3\ln x\ +\ 8\ln y$ 

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

•  $\ln\left(x^3y^8\right)$  

•  $24\ln\left(xy\right)$  

•  $11\ln\left(xy\right)$