PROBLEMS ON SOLVING LOGARITHMIC EQUATIONS

Problem 1 :

Solve for x :

log₂ (x + 2) + log₂ (3) = log₂ (27)

Solution :

Problem 2 :

Solve for x :

log₃ x + log₃ (x - 2) = log₃ (x + 10)

Solution :

Problem 3 :

Solve for x :

ln (e^{x + 7}) = 10

Solution :

Problem 4 :

Solve for x :

Solution :

Problem 5 :

Solve for x :

Solution :

Problem 6 :

Solve for x in terms of y :

log x + log y = log (x + y)

Solution :

Problem 7 :

Given : log₄ (x² + x) - log₄ (x + 1) = 2. Find x.

A)  16  

B)  0

C)  -1

D)  None of these

Solution :

Problem 8 :

If log₂ x + log₄ x = 6, then the value of x is

A)  16

B)  32

C)  64

D)  128

Solution :

Problem 9 :

Solve for x :

log₂ x + log₄ x + log₁₆ x = 21/4

Solution :

Problem 10 :

What are the restrictions on b, so that x has two solutions in the given logarithmic equation?

Solution :

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