Properties of Logarithms

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.HSF.BF.B.5

CCSS.HSF.IF.C.8

Write log_b(x/y) 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

Rewrite log_b(xⁿ)

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

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.C.8

Write the expression as a single logarithm.   Then simplify if possible.
log₅3 + log₅6 + log₅9

• log₅69
• log₅56
• log₅162
• log₅98

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

Write the expression as a single logarithm.   Then simplify if possible.
log 6 - log 3 + 2 log 7

• log 98
• log 78
• log 56
• log 45

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Condense

• A
• B
• C
• D

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

Expand

• A
• B
• C
• D

Tags

CCSS.HSN.RN.A.1

Condense

• A
• B
• C
• D

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

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

• 6log₈(xyz)
• log₈(x) - log₈(y) - 6log₈(z)
• log₈(x) + log₈(y) - log₈(z)
• log₈(x) + log₈(y) + 6log₈(z)

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2