Exponential and Logarithmic Equations

Rewrite log_pt = m in exponential form.

• p^t = m
• t^m = p
• m^t = p
• p^m = t

Tags

CCSS.HSF.BF.B.5

Write the exponential equation as a logarithm
6³=216

• log₆(3) = 216
• log₃(6) = 216
• log₆(216)=3
• log₂₁₆(6)=3

Tags

CCSS.HSF.BF.B.5

Evaluate log₅  20 to the third decimal place

• 0.537
• 2.996
• 1.301
• 1.861

Tags

CCSS.HSF.BF.B.5

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)
• log₂(xy⁵)
• log₂(x/y)⁵
• log₂(x/5y)

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

4^{3x + 5} = 16

• -5/3

• -1

• -3/2

• 2/3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.LE.A.4

Solve log₂ (2 - 2x) + log₂ (1 - x) = 5

• 4

• 5

• -2

• -3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

Solve log₅ (x + 3) = log₅ x + log₅ 3

• 3/2

• 9/2

• 2/3

• No Solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve 2.8^x = 41

• 0.277

• 3.607

• -0.282

• 3.684

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve log₂ (x² - 1) = 3 + log₂ (x - 1)

• 4

• 2

• 1

• 7

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Find the time required for an investment of $1000 to grow to $5000 at an interest rate of 8% per year compounded monthly. (round to nearest year)

• 1 year
• 242 years
• 20 years
• 13 years

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.4