Logarithms

Write as a single logarithm, then simplify.

log₃9 + log₃27

• -1

• 5

• 4

• 1

Answer explanation

$\log_3\left(9\cdot27\right)=\log_3\left(3^5\right)=5\cdot\log_33=5\cdot1=5$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Write as one logarithm, then simplify.

log₆3 + log₆2

• 0

• log₆5

• log₆1

• 1

Answer explanation

$\log_6\left(2\right)+\log_6\left(3\right)=\log_6\left(2\cdot3\right)=\log_6\left(6\right)=1$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Evaluate.

3 log₂4

• 3

• 6

• 2

• 4

Answer explanation

$3\log_24=3\cdot\log_2\left(2^2\right)=3\cdot2\log_22=3\cdot2\cdot1=6$

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Evaluate log₄1

• 1
• 0
• 4
• undefined

Tags

CCSS.HSF.BF.B.5

Write in logarithmic form.
5² = 25

• log₅2 = 25
• log₂25 = 5
• log₂₅5 = 2
• log₅25 = 2

Tags

CCSS.HSF.BF.B.5

Write in exponential form.

 $\log_2\left(\frac{1}{8}\right)=-3$  

•  $2^{-3}=\frac{1}{8}$  

•  $2^{\frac{1}{8}}=-3$  

•  $-3^2=\frac{1}{8}$  
  

•  $-3^{\frac{1}{8}}=2$  
  

Tags

CCSS.HSF.BF.B.5

Write the logarithm expression as a single logarithm

log₅4 + log₅3

• log₅7

• log₅12

• log₇5

• 3log₅4

Answer explanation

$\log_5\left(4\cdot3\right)$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Write the logarithm expression as a single logarithm

log₄60 - log₄4 + log₄x

• log₄15

• log₄15x

• log₄56x

• xlog₄30

Answer explanation

$\log_4\left(60\div4\cdot x\right)$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Expand the logarithm expression

log 6x³y

• log 6x³ + log y

• log 6 + log x³ + log y

• 3 log 6 + log x + log y

• log 6 + 3log x + log y

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand the logarithm expression

 $\log\left(\frac{5x}{4y}\right)$  

• log 5x + log 4y

• log 5x - 4log y

• (log 5 + log x) - (log 4 + logy)

• 5log x - 4 logy

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8