log(3)(3x+8)=log(3)(x^2+x)

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


Simplifying
log(3)(3x + 8) = log(3)(x2 + x)

Reorder the terms:
glo * 3(8 + 3x) = log(3)(x2 + x)

Reorder the terms for easier multiplication:
3glo(8 + 3x) = log(3)(x2 + x)
(8 * 3glo + 3x * 3glo) = log(3)(x2 + x)
(24glo + 9glox) = log(3)(x2 + x)

Reorder the terms:
24glo + 9glox = glo * 3(x + x2)

Reorder the terms for easier multiplication:
24glo + 9glox = 3glo(x + x2)
24glo + 9glox = (x * 3glo + x2 * 3glo)
24glo + 9glox = (3glox + 3glox2)

Solving
24glo + 9glox = 3glox + 3glox2

Solving for variable 'g'.

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

Add '-3glox' to each side of the equation.
24glo + 9glox + -3glox = 3glox + -3glox + 3glox2

Combine like terms: 9glox + -3glox = 6glox
24glo + 6glox = 3glox + -3glox + 3glox2

Combine like terms: 3glox + -3glox = 0
24glo + 6glox = 0 + 3glox2
24glo + 6glox = 3glox2

Add '-3glox2' to each side of the equation.
24glo + 6glox + -3glox2 = 3glox2 + -3glox2

Combine like terms: 3glox2 + -3glox2 = 0
24glo + 6glox + -3glox2 = 0

Factor out the Greatest Common Factor (GCF), '3glo'.
3glo(8 + 2x + -1x2) = 0

Factor a trinomial.
3glo((4 + -1x)(2 + x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(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.

Subproblem 3

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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