Find all real solutions.

Question

Find all real solutions to the equation log4(3x^2) - log4(4x+8) = -1

Be sure to check any potential solutions in the original equation.

Answer 1

log₄(3x²) - log₄(4x + 8) = -1

log₄ [3x² / (4x+8)] = -1

3x² / (4x+8) = 4^-1 = 1/4

3x² / (4x+8) = 1/4

(3x²)(4) = (4x+8)(1)

12x² - 4x - 8 = 0

3x² - x - 2 = 0

(3x + 2)(x - 1) = 0 So, x = -2/3, 1

Answer 2

First contract the left side using Laws of Logrithms.

Then convert to exponential form

Set eqution to zero and solve using Zero Product Rule.