Condense and expand logarithms (quotients and products)

Which of the following illustrates the Product Property of Logarithms

• log₃(x) ⋅ log₃(y) = log₃(x+y)

• log₃(x) ⋅ log₃(y) = log₃(xy)

• log₃(x) + log₃(y) = log₃(xy)

Which of the following illustrates the Quotient Property of Logarithms

• log₄(x ÷ y) = log₄(x) - log₄(y)

• log₄(x ÷ y) = log₄(x) ÷ log₄(y)

• log₄(x - y) = log₄(x) ÷ log₄(y)

Tags

CCSS.HSF.BF.B.5

Expand the following:  $\log_24g$  

•  $\log_24\times\log_2g$  

•  $\log_24+\log_2g$  

•  $\log_24-\log_2g$  

•  $\frac{\log_24}{\log_2g}$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

Expand the following:  $\log\frac{n}{m}$  

•  $n\log m$  

•  $\log n+\log m$  

•  $\log n-\log m$  

•  $\frac{\log n}{\log m}$  

Condense the Logarithm:  $\log_4x+\log_4y$  

•  $4\log xy$  

•  $\log_4xy$  

•  $y\log_4x$  

•  $\log_4\ \frac{x}{y}$  

Tags

CCSS.HSF.LE.A.4

Condense the Logarithm:  $\log_4x-\log_4y$  

•  $4\log_{ }xy$  

•  $\log_4xy$  

•  $y\log_4x$  

•  $\log_4\ \frac{x}{y}$  

Tags

CCSS.HSA.SSE.B.3

Expand the following:  $\log_5\left(\frac{4xy}{z}\right)$  

•  $\log_54x+\log_5y-\log_5z$  

•  $\log_54+\log_5x+\log_5y-\log_5z$  

•  $\log_54xy-\log_5z$  

•  $\frac{\log_54xy}{\log_5z}$  

Expand the following:  $\log_2\frac{x}{6y}$  

•  $\frac{\log_2x}{\log_26y}$  

•  $\log_2x+\log_26y$  

•  $\log_2x-\log_26-\log_2y$  

•  $\log_2x-\log_26+\log_2y$  

Write as one logarithm. Simplify, if possible.
log₆3 + log₆2

• 0
• log₆5
• log₆1
• 1

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

Condense into a single log and simplify

 $\log_280-\log_25$  

•  $\log_275$  
  

•  $\log_2400$  
  

• 8

• 4