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.HSA.SSE.B.3

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

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.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

CCSS.HSA.SSE.A.2

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.HSF.IF.C.8

Write in change of base log_bx

• (log_ax)/(log_ab)
• (log_ax)(log_ab)
• (log_ax)+(log_ab)
• (log_ax)-(log_ab)

Tags

CCSS.HSF.LE.A.4

Evaluate log_b(1)

• 0
• 1
• -1
• b

Tags

CCSS.HSF.BF.B.5

Evaluate log_b(b)

• -1
• 0
• 1
• b

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Evaluate b^log_b(x)

• x
• b
• 1
• 0

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Rewrite log_b(a) with base a

• 1/(log_ab)
• -log_ba
• 1/(log_ba)
• -log_ab

Evaluate log_b(b^x)

• 1
• 0
• x
• b

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

log_bx=y iff _______

• b^y=x
• log_by=x
• b^x=y
• log_xb=y

Tags

CCSS.HSF.BF.B.5