Properties of Logarithms

Condense: log₂6+log₂3=

• log₂18

• log₂2 = 1

• log₂3

• log₂9

Tags

CCSS.HSF.BF.B.5

Write log_b(xy) as two logs

• log_bx+log_by
• log_bx-log_by
• log_bx*log_by
• log_bx/log_by

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.C.8

Expand

• A
• B
• C
• D

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.LE.A.4

Condense

• logxyz³
• log(xy/z³)
• logx+logy+logz³
• logx³y³z³

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Expand

• log₈x+log₈y+log₈z
• 5log₈x+5log₈y+5log₈z
• log₈xy+5log₈z
• log₈x+log₈y+5log₈z

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

Evaluate log_b(b)

• -1
• 0
• 1
• b

Tags

CCSS.HSF.BF.B.5

Rewrite log_b(xⁿ)

• nlog_bx
• (log_bx)ⁿ
• xⁿlog_bx
• log_b(xⁿ)

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

Expand.

• 1/3 log x + log y + log z
• 1/3 log x + 1/3 log y + 1/3 log z
• 1/3 log x - 1/3 log y - 1/3 log z
• 3 log x + 3 log y + 3 log z

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.C.8

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

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

Expand log₃(9x²)

• 3+2log₃x

• log₃9+2log₃x

• 2+2log₃x

• log9+2logx

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.C.8