SOLVING LOGARITHMIC EQUATIONS WORKSHEET

Solve logarithmic equations :

1)  log₇ 3 + log₇ x = log₇ 32                   Solution

2)  2 log₆ 4x = 0                 Solution

3)  log₂ x + log₂ (x - 3) = 2                 Solution

4)  log₂ (x + 5) - log₂ (x - 2) = 3                 Solution

5)  4 ln (2x + 3) = 11                 Solution

6)  log x - log 6 = 2 log 4                 Solution

7)  log 2x = 1.5                 Solution

8)  log₂ 2x = -0.65                 Solution

9)  1/3 log₂ x + 5 = 7                 Solution

10)  4 log₅ (x + 1) = 4.8                 Solution

11)  log₂ x + log₂ 3 = 3                 Solution

12)  2 log₄ x - log₄ (x - 1) = 1                 Solution

Find the value of y.

Solution

Solve the following logarithmic equations.

Problem 1 :

2 logx = log 2 + log (3x - 4)

Solution

Problem 2 :

log x + log(x - 1) = log(4x)

Solution

Problem 3 :

log₃ (x + 25) - log₃ (x - 1) = 3

Solution

Problem 4 :

log₉ (x - 5) + log₉ (x + 3) = 1

Solution

Problem 5 :

log x + log (x - 3) = 1

Solution

Problem 6 :

log₂ (x - 2) + log₂ (x + 1) = 2

Solution

Problem 7 :

ln x = -3

Solution

Problem 8 :

log(3x - 2) = 2

Solution