Properties of Logs

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

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

• 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

Logarithmic functions are the inverse of...

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

Tags

CCSS.HSF.BF.B.5

Expand log₆(5x³/y).

• log₆5x³-log₆y
• log₆5+log₆x³-log₆y
• log₆5+3log₆x-log₆y

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand.

• 1/3 log x + log y + log z
• 1/3 log x + 1/3 log y + 1/3 log z
• 1/3 log x - 1/3 log y - 1/3 log z
• 3 log x + 3 log y + 3 log z

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

• log(x) + log(z) + 4log(y)
• 3log(x) − log(z) − 4log(y)
• 3log(x) + log(z) + 4log(y)
• log(x) − 4log(z) − 3log(y)

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

• log₅(x²z²y¹⁰)
• log₅(z²y²x¹⁰)
• log(zy²x¹⁰)
• log₅(z² + y² + x¹⁰)

Tags

CCSS.HSF.BF.B.5

• 2ln(x) + ln(y)
• 4ln(x) + 2ln(y)
• 2ln(x) - 2ln(y)
• 4ln(xy)

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Expand the logarithm

• ln(x)+1/2ln(x+2)

• 1/2ln(x) + 1/2ln(x+2)

• ln(x²)-ln(x+2)

• ln(x)+1/2ln(x)+1/2ln(2)

Condense into one logarithm

• $\log\sqrt{x}\left(x+1\right)^3$

• $\log x\left(x+1\right)^3$

• $\frac{1}{2}\log\left(x+\left(x+1\right)^3\right)$

• $\log\left(x\right)$