Solving Logarithmic Equations Quiz

What is the solution to the equation?

log₅(5x + 9) = log₅(6x)

• x = 9

• x = -9

• x = 0

• x = 1

• x = 3

Answer explanation

Solve the equation for w.

log₉(6−3w) = log₉(-2w)

CONDENSE the logarithm.

Use the One-to-One Property: If log_bm = log_bn, then m = n.

​ (a)   = ​ (b)  

SOLVE and CHECK FOR EXTRANEOUS SOLUTIONS.

w = ​ (c)  

because

​ (d)  

• 6−3w
• -2w
• No Solution
• 6
• 0
• 9
• w
• 6w
• logarithms cannot have negative values
• logarithms cannot have negative bases

Answer explanation

Solve the equation for a.

3⋅log₇4 = log₇(4a−8)

CONDENSE the logarithm.

log₇​ ​ (a)   = log₇(4a−8)

Use the One-to-One Property: If log_bm = log_bn, then m = n.

​ (b)   = ​ ​ (c)  

SOLVE and CHECK FOR EXTRANEOUS SOLUTIONS.

a = ​ ​ (d)  

• 64
• 81
• 2
• 12a
• 18
• 4a−8
• 89

Answer explanation

Solve for m.

log₄(m²) = log₄(18 - 7m)

Select all correct solutions.

• -9

• -2

• 2

• 9

• 0

Answer explanation

Solve for p.

log₃(2p−5) = 2⋅log₃6 − log₃4

Select all correct solutions.

• -7

• -2

• 7

• 2

• 0

Answer explanation

Solve for k.

log 2 + log (k²) = log (k² + 16)

Select all correct solutions.

• k = 4

• k = -4

• k = 2

• k = -2

• k = 0

Answer explanation

Solve for x.

log₃(4x + 8) − 7 = -3

(Remember to check for extraneous solutions!)

• x = 14

• x = 18

• x = 2

Answer explanation

Solve for x.

log₂(x − 4) = 6

• 64

• 68

• 62

• 16

• 8

Answer explanation

Tags

CCSS.HSF.BF.B.5

Solve for x.

log (2x) + log (x−5) = 2

(Remember to check for extraneous solutions!)

• x = 10

• x = 5

• x = 15

• x = -5

• x = -10

Answer explanation

Solve for x.

2·log x − log 4 = 2

(Remember to check for extraneous solutions!)

• x = -20

• x = 4

• x = -40

• x = 40

• x = 20

Answer explanation