logarithmic properties review; expand and condense

Condense the expression as a single logarithm.

log₅ 3 + log₅ 6 + log₅ 9

• log₅ 69

• log₅ 56

• log₅ 162

• log₅ 98

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Condense  $5\ \log_2\ 12$  

•  $\log_2\ \frac{12}{5}$  

•  $\log_5\ \sqrt{12}$  

•  $\log_2\ 12^5$  

•  $\log_2\left(12\times5\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Condense:  $\log_3\left(x\right)+\log_3\left(y\right)$  

•  $\log_3\left(x\right)\cdot\log_3\left(y\right)$  

•  $\log_3\left(xy\right)$  

•  $\log_3\left(\frac{x}{y}\right)$  

•  $\frac{\log_{3\ }x}{\log_3\ y}$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Condense:  $2\log_5\left(x\right)+3\log_5\left(y\right)$  

•  $\log_5\left(x^2\right)+\log_5\left(y^3\right)$  

•  $\log_5\left(2x\right)+\log_5\left(3y\right)$  

•  $2\log_5\left(x\right)\cdot3\log_5\left(y\right)$  

•  $\log_5\left(x^2y^3\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Expand  $\log_6\left(7x^5y\right)$  

•  $\log_6\left(7\right)+\log_6\left(x^5\right)+\log_6\left(y\right)$  

•  $\log_6\left(7\right)+5\log_6\left(x\right)+\log_6\left(y\right)$  

•  $\log_6\left(7x^5\right)+\log_6\left(y\right)$  

•  $5\log_6\left(7x\right)+\log_6\left(y\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Expand

• 4 ln 3y - 3 lnx

• ln3 + 4 lny - 3 lnx

• 4 ln x 3 lny - 3 lnx

• ln3 + lny⁴ - lnx³

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand log (ab)

• log a x log b

• log a + log b

• log a - log b

• a log b

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Expand  $\log\left(\frac{a}{b}\right)$  

• log a - log b

•  $\frac{\log a}{\log b}$  

• log_a b

• log_b a

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Expand  $\log\left(a^2b\right)$  

• 2log(a) + log(b)

• 2log(a) + 2log(b)

• log(a) + log(b)

• 2log(a) * log(b)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

• $\log\left(xy^3\right)$

• $\log\left(x^6-y^3\right)$

• $\log\left(\frac{x^6}{y^3}\right)$

• $\log\left(x^6y^3\right)$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5