2log(3x)+log(x+2)=log(9x^2+18x)

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Solution for 2log(3x)+log(x+2)=log(9x^2+18x) equation: 


Simplifying
2log(3x) + log(x + 2) = log(9x2 + 18x)

Remove parenthesis around (3x)
2glo * 3x + log(x + 2) = log(9x2 + 18x)

Reorder the terms for easier multiplication:
2 * 3glo * x + log(x + 2) = log(9x2 + 18x)

Multiply 2 * 3
6glo * x + log(x + 2) = log(9x2 + 18x)

Multiply glo * x
6glox + log(x + 2) = log(9x2 + 18x)

Reorder the terms:
6glox + glo(2 + x) = log(9x2 + 18x)
6glox + (2 * glo + x * glo) = log(9x2 + 18x)
6glox + (2glo + glox) = log(9x2 + 18x)

Reorder the terms:
2glo + 6glox + glox = log(9x2 + 18x)

Combine like terms: 6glox + glox = 7glox
2glo + 7glox = log(9x2 + 18x)

Reorder the terms:
2glo + 7glox = glo(18x + 9x2)
2glo + 7glox = (18x * glo + 9x2 * glo)
2glo + 7glox = (18glox + 9glox2)

Solving
2glo + 7glox = 18glox + 9glox2

Solving for variable 'g'.

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

Add '-18glox' to each side of the equation.
2glo + 7glox + -18glox = 18glox + -18glox + 9glox2

Combine like terms: 7glox + -18glox = -11glox
2glo + -11glox = 18glox + -18glox + 9glox2

Combine like terms: 18glox + -18glox = 0
2glo + -11glox = 0 + 9glox2
2glo + -11glox = 9glox2

Add '-9glox2' to each side of the equation.
2glo + -11glox + -9glox2 = 9glox2 + -9glox2

Combine like terms: 9glox2 + -9glox2 = 0
2glo + -11glox + -9glox2 = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(2 + -11x + -9x2) = 0


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 '(2 + -11x + -9x2)' equal to zero and attempt to solve:

Simplifying
2 + -11x + -9x2 = 0

Solving
2 + -11x + -9x2 = 0

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

Add '-2' to each side of the equation.
2 + -11x + -2 + -9x2 = 0 + -2

Reorder the terms:
2 + -2 + -11x + -9x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -11x + -9x2 = 0 + -2
-11x + -9x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-11x + -9x2 = -2

Add '11x' to each side of the equation.
-11x + 11x + -9x2 = -2 + 11x

Combine like terms: -11x + 11x = 0
0 + -9x2 = -2 + 11x
-9x2 = -2 + 11x

Add '9x2' to each side of the equation.
-9x2 + 9x2 = -2 + 11x + 9x2

Combine like terms: -9x2 + 9x2 = 0
0 = -2 + 11x + 9x2

Simplifying
0 = -2 + 11x + 9x2

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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