Logs and Exponential Functions

log 3 12 + log 3 4

• log 48 / log 3 = 3.524

• log 3 / log 48 = .284

• log 12 / log 4 = 3

• log 48 / log 4 = 2.792

log ₃ 343 - log ₃ 49
Step 1: ???         Quotient Prop
Step 2: log ₃ 7 
log 7 / log 3 = 1.771

• log ₃ (343 - 49)

• log ₃ (343 / 49)

• log ₃ (343 * 49)

e^x = 32

• e^32 = x, rhino

• e / 32 = x, x = .085

• ln 32 = x, x = 3.466

• elephant

Tags

CCSS.HSF.BF.B.5

Use change of base to solve:
log ₁₇ 132

• log 17 / log 132

• 132 / 17

• log 132 / log 17

log ₃ (4x+140) = log ₃ 156

• Cancel logs
  4x + 140 = 156
  x=16

• Combine log ₃ 
  log ₆ 4x + 140 +156 = 0
  log ₆ 4x = 296
  x=74

• Cancel logs
  4x + 140 = 156
  x= 4

log₂(2) + log₂(8x) = 6

• x = 3

• x = 2

• x = 6

• x = 4

Solve:
log₉(x)+log₉(x+2)=log₉(35)

• 5

• -7

• 5, -7

• -7, -13

log₄(3x-1)=log₄(2x+3)

• 4

• 3

• 1

• 8

log₆(2x + 3) = 3

• x = 106.5

• x = 100

• x = 16

• x = 50

Tags

CCSS.HSF.BF.B.5

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

• Growth

• Decay

Tags

CCSS.HSF-IF.C.8B