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.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Rewrite log_b(xⁿ)

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

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

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.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

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

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

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

• log (a⁵ + b²⁵)
• log (a⁵ − b²⁵)
• log (ab²⁵)
• log (a⁵/b²⁵)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

• log(x) + log(z) + 4log(y)
• 3log(x) − log(z) − 4log(y)
• 3log(x) + log(z) + 4log(y)
• log(x) − 4log(z) − 3log(y)

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

• 24log(u) - log(v)
• 24log(u) + 6log(v)
• 4log(u) + 6log(v)
• 4log(u) - 6log(v)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

• 60 log(ab)
• 6log(a) + log(b)
• log(a) - 30 log(b)
• 6log(a) + 30 log(b)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5