log^13(x^2-4)=log^13(3x)

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Solution for log^13(x^2-4)=log^13(3x) equation:


Simplifying
log13(x2 + -4) = log13(3x)

Reorder the terms:
g13lo(-4 + x2) = log13(3x)
(-4 * g13lo + x2 * g13lo) = log13(3x)
(-4g13lo + g13lox2) = log13(3x)

Remove parenthesis around (3x)
-4g13lo + g13lox2 = g13lo * 3x

Reorder the terms for easier multiplication:
-4g13lo + g13lox2 = 3g13lo * x

Multiply g13lo * x
-4g13lo + g13lox2 = 3g13lox

Solving
-4g13lo + g13lox2 = 3g13lox

Solving for variable 'g'.

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

Add '-3g13lox' to each side of the equation.
-4g13lo + -3g13lox + g13lox2 = 3g13lox + -3g13lox

Combine like terms: 3g13lox + -3g13lox = 0
-4g13lo + -3g13lox + g13lox2 = 0

Factor out the Greatest Common Factor (GCF), 'g13lo'.
g13lo(-4 + -3x + x2) = 0

Factor a trinomial.
g13lo((-1 + -1x)(4 + -1x)) = 0

Subproblem 1

Set the factor 'g13lo' equal to zero and attempt to solve: Simplifying g13lo = 0 Solving g13lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g13lo = 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 '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Add 'x' to each side of the equation. -1x + x = 1 + x Combine like terms: -1x + x = 0 0 = 1 + x Simplifying 0 = 1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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