USE THE ONE TO ONE PROPERTY OF LOGARITHMS TO SOLVE

Use the One-to-One Property to solve the equation for x.

Problem 1 :

log₂(x + 1) = log₂ 4

Solution:

log₂(x + 1) = log₂ 4

Use One to One Property,

x + 1 = 4

x = 4 - 1

x = 3

Problem 2 :

log₂(x - 3) = log₂ 9

Solution:

log₂(x - 3) = log₂ 9

Use One to One Property,

x - 3 = 9

x = 9 + 3

x = 12

Problem 3 :

log(2x + 1) = log 15

Solution:

log(2x + 1) = log 15

Use One to One Property,

2x + 1 = 15

2x = 14

x = 14/2

x = 7

Problem 4 :

log(5x + 3) = log 12

Solution:

log(5x + 3) = log 12

Use One to One Property,

5x + 3 = 12

5x = 9

x = 9/5

Problem 5 :

ln(x + 2) = ln 6

Solution:

ln(x + 2) = ln 6

Use One to One Property,

x + 2 = 6

x = 6 - 2

x = 4

Problem 6 :

ln(x - 4) = ln 2

Solution:

ln(x - 4) = ln 2

Use One to One Property,

x - 4 = 2

x = 2 + 4

x = 6

Problem 7 :

ln(x² - 2) = ln 23

Solution :

ln(x² - 2) = ln 23

Use One to One Property,

x² - 2 = 23

x² = 25

x = ±5

Problem 8 :

ln(x² - x) = ln 6

Solution:

ln(x² - x) = ln 6

Use One to One Property,

x² - x = 6

x² - x - 6 = 0

(x - 3) (x + 2) = 0

x = 3 or x = -2