Test Review: 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

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

Solve for x.
 $-6\log_{12}\left(x-5\right)=-6$  

• -1

• -864

• 2

• 17

Tags

CCSS.HSF.BF.B.5

Solve for x

log₅(4x - 7) = log₅(x + 5)

• 3

• 12

• 4

• 7

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSF.BF.B.5

Solve for x:  $9^x=60$  

• 1.748

• x = 6.667

• x = 0.537

• x = 1.863

Tags

CCSS.HSF.LE.A.4

Solve for x:
4^2x + 1 = 17

• x = 1
• x = -1
• x = 2
• x = -2

Tags

CCSS.7.EE.B.4A

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

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