Log Properties

When a logarithm has division inside of it, it expands using ________________.

• Addition
• Subtraction
• Multiplication
• Division

log (-1) = 

• 0.1
• .01
• all real numbers
• does not exist

Tags

CCSS.HSF.BF.B.5

Write log_b(xy) as two logs

• log_bx+log_by
• log_bx-log_by
• log_bx*log_by
• log_bx/log_by

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

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.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Rewrite log_b(xⁿ)

• nlog_bx
• (log_bx)ⁿ
• xⁿlog_bx
• log_b(xⁿ)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Write the expression as a single logarithm.   Then simplify if possible.
log₅3 + log₅6 + log₅9

• log₅69
• log₅56
• log₅162
• log₅98

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Write the expression as a single logarithm.   Then simplify if possible.
log 6 - log 3 + 2 log 7

• log 98
• log 78
• log 56
• log 45

Tags

CCSS.HSA.SSE.B.3

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