Properties of Logs

log(4x)

• log4-logx

• log4+logx

• 4logx

• xlog4

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

log(xy²)

• logx+2logy

• logx+logy²

• logx-2logy

• logx+logy+log2

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

 $\log\left(\frac{x}{y}\right)$  

• 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.B.3

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

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

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.B.3

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

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

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

Tags

CCSS.HSF.BF.B.5

Expand the following logarithmic expression:  $\log\left(\sqrt{\frac{x}{y}}\right)$  

•  $\log\left(x\right)-\log\left(y\right)$  

•  $\frac{1}{2}\log\left(x\right)-\frac{1}{2}\log\left(y\right)$  

•  $2\log\left(x\right)-2\log\left(y\right)$  

•  $\frac{\frac{1}{2}\log\left(x\right)}{\frac{1}{2}\log\left(y\right)}$  

•  $\frac{1}{2}\log\left(x\right)+\frac{1}{2}\log\left(y\right)$