Basic Properties of Logarithms

The common logarithm has what base?

• 10
• 0
• e
• -e

Tags

CCSS.HSF.BF.B.5

The natural logarithm has what base?

• 10

• 0

• e

• -e

Tags

CCSS.HSF.BF.B.5

Write $\log_b\left(xy\right)$  as two logs.

•  $\log_bx+\log_by$  

•  $\log_bx-\log_by$  

•  $\log_bx\times\log_by$  

•  $\frac{\log_bx}{\log_by}$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Write $\log_b\left(\frac{x}{y}\right)$  as two logs.

•  $\log_bx+\log_by$  

•  $\log_bx-\log_by$  

•  $\log_bx\times\log_by$  

•  $\frac{\log_bx}{\log_by}$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Rewrite $\log_b\left(x^n\right)$ .

•  $n\log_bx$  

•  $\left(\log_bx\right)^n$  

•  $x^n\log_bx$  

•  $x\log_bn$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Condense

• A

• B

• C

• D

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Condense

• A

• B

• C

• D

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Write as a single log: log 12 + 2 log x

• log (12 + 2x)
• log (14x)
• log (12 * 2x)
• log (12x²)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

• log₅(x²z²y¹⁰)
• log₅(z²y²x¹⁰)
• log(zy²x¹⁰)
• log₅(z² + y² + x¹⁰)

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Condense

• A

• B

• C

• D

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3