Properties of Logarithms

Condense

• A
• B
• C
• D

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Condense

• A
• B
• C
• D

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Expand log₆(5x³/y).

• log₆5x³-log₆y
• log₆5+log₆x³-log₆y
• log₆5+3log₆x-log₆y

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.C.8

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

• log₅69
• log₅56
• log₅162
• log₅98

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

Condense

• A
• B
• C
• D

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)

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.C.8

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.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.C.8