log^4(3x-1)=log^4(2x+8)

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Solution for log^4(3x-1)=log^4(2x+8) equation:


Simplifying
log4(3x + -1) = log4(2x + 8)

Reorder the terms:
g4lo(-1 + 3x) = log4(2x + 8)
(-1 * g4lo + 3x * g4lo) = log4(2x + 8)
(-1g4lo + 3g4lox) = log4(2x + 8)

Reorder the terms:
-1g4lo + 3g4lox = g4lo(8 + 2x)
-1g4lo + 3g4lox = (8 * g4lo + 2x * g4lo)
-1g4lo + 3g4lox = (8g4lo + 2g4lox)

Solving
-1g4lo + 3g4lox = 8g4lo + 2g4lox

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Add '-8g4lo' to each side of the equation.
-1g4lo + -8g4lo + 3g4lox = 8g4lo + -8g4lo + 2g4lox

Combine like terms: -1g4lo + -8g4lo = -9g4lo
-9g4lo + 3g4lox = 8g4lo + -8g4lo + 2g4lox

Combine like terms: 8g4lo + -8g4lo = 0
-9g4lo + 3g4lox = 0 + 2g4lox
-9g4lo + 3g4lox = 2g4lox

Add '-2g4lox' to each side of the equation.
-9g4lo + 3g4lox + -2g4lox = 2g4lox + -2g4lox

Combine like terms: 3g4lox + -2g4lox = 1g4lox
-9g4lo + 1g4lox = 2g4lox + -2g4lox

Combine like terms: 2g4lox + -2g4lox = 0
-9g4lo + 1g4lox = 0

Factor out the Greatest Common Factor (GCF), 'g4lo'.
g4lo(-9 + x) = 0

Subproblem 1

Set the factor 'g4lo' equal to zero and attempt to solve: Simplifying g4lo = 0 Solving g4lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g4lo = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Add '-1x' to each side of the equation. x + -1x = 9 + -1x Combine like terms: x + -1x = 0 0 = 9 + -1x Simplifying 0 = 9 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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