Logarithm Properties

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 (6⁶ * 5⁶)

• log 11 +(log6/2) + (log 5/2)
• 6 log 6 - 36 log 5
• 6 log 6 + 36 log 5
• 6 log 6 + 6 log 5

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

log₃(6*11*7⁵)

• 5log₃6+5log₃11
• log₃7+log₃6/2+log₃11/2
• log₃6+log₃11+5log₃7
• 5log₃7+log₃6/2

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

log(x³*y)³

• 3 log z +log x/ 2
• 3 log-9log y
• 9 log x + 3 log y
• 3 log x - 3 log y

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

log₂(u⁶/v⁶)

• 6 log₂u + 36 log₂v
• 6 log₂ u+6 log₂ v
• 6log₂u-6log₂v

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

log₆(8²*3)⁶

• log₆8+log₆3+2log₆11
• 2log₆8+6log₆3
• 12log₆8+6log₆3

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

log₄(8⁵*11³)

• 15log₄8-3log₄11
• 5log₄8+3log₄11
• 5log₄8-3log₄11

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8