Properties of Logarithms

Expand log₅(u³v⁵)

• 1/2(log₅u+log₅v+log₅uw)
• 5 log₅ u - 15 log₅ v 
• log₅u + log₅v +3 log₅w
• 3 log₅u + 5 log₅v

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

log (7 * 12 ²) ⁵ 

• (log7/2)+ (log 12/2) + (log11/2)
• 5 log 7 +10 log 12
• 2 log 11 + log 7/2
• 10 log 7 - 5 log 12

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

log (u⁶/v)³

• log u/2 + log v /2 + log w /2
• 3 log u - 18 log v
• 18 log u + 3 log v
• 18 log u - 3 log v

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

log₃(x³/y)²

• 6log3x-2log₃y
• 2log₃x-6 log₃y
• log₃z +log₃x/3+log₃y/3
• 2log₃x+6log₃y

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Condense the expression to a single logarithm.
16 log u +4 log v 

• log(v⁴u¹⁶)
• log(v⁴u⁴)
• log(vuw⁴)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

12 log u + 3 log v

• log(v³u¹²)
• log(vuw⁴)
• log(u³/v¹²)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

24 log₄3-6log₄8

• log₄(3⁴/8)
• log₄(8⁶*3²⁴)
• log₄(3²⁴/8⁶)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

2 log a+3 log b

• log(b³*a²)
• log(a³/b⁶)
• log(bac²)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

18 log x- 3 log y

• log(y³x¹⁸)
• log(x¹⁸/y³)
• log(yxz⁶)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

log₂(2/3²)

• log₂(2)-log₂(3²)
• log₂(2)-2log₂(3)
• log₂(2) + 2log₂(3)
• log₂(2)*log₂(3²)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5