Logarithmic & Exponential Equations Review

The solution to the equation log₇(x + 13) = log₇(3 - x) is x = (a)   .

• x = -5
• x = 5
• No solution
• All real numbers

Solve the equation: log₂(n² + 13) = log₂(n - 1) + log₂(n + 3).

• n = 8

• n = 7

• n = -8

• n = 16

Solve the equation: 2 · ln(a + 3) = (1/4) · ln16 + ln(a + 7) and determine the value of a.

• a = 1

• a = 2

• a = -5

• a = 0

Match the following equations with their solutions.

• Solve the equation:

  x² - 5x + 6 = 0.

• -5

• Solve the equation:

  log(3c + 4) - log(c - 6) = log(c + 6).

• 8

• Solve the equation:

  x + 2 = 12.

• 6

• Solve the equation:

  2x + 3 = 1.

• 10

Match the following equations with their solutions.

• Solve the equation: log_2(5v + 23) - 9 = -2.

• 23

• Solve the equation: log_2(5v + 23) - 9 = -3.

• 20

• Solve the equation: log_2(5v + 23) - 9 = -5.

• 21

• Solve the equation: log_2(5v + 23) - 9 = -4.

• 105

The solution to the equation log₁₆(p + 5) - log₁₆(p - 2) = 1/2 is p = (a)  

• p = (7√6 + 17)/5
• p = (5 + 2√6)/(√6 + 1)
• p = (7√6 - 17)/5
• p = (17 - 7√6)/5

Solve the equation: (1/3) · log₃ 64 + 2 · log₃ n = 2. Choose the value of n.

• 1

• 3/2

• 2

• 9/4

• x = 5/2

• x = 2

• x = 3

• x = -3

• x = -6

• x = 6

• x = 2

• x = -2

• x = ln(90)/ln(5) - 1

• x = ln(45)/ln(5)

• x = ln(90)/ln(10)

• x = ln(90) - ln(5)