log(2x+3)+log(x-2)=2logx

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Solution for log(2x+3)+log(x-2)=2logx equation:


Simplifying
log(2x + 3) + log(x + -2) = 2logx

Reorder the terms:
glo(3 + 2x) + log(x + -2) = 2logx
(3 * glo + 2x * glo) + log(x + -2) = 2logx
(3glo + 2glox) + log(x + -2) = 2logx

Reorder the terms:
3glo + 2glox + glo(-2 + x) = 2logx
3glo + 2glox + (-2 * glo + x * glo) = 2logx
3glo + 2glox + (-2glo + glox) = 2logx

Reorder the terms:
3glo + -2glo + 2glox + glox = 2logx

Combine like terms: 3glo + -2glo = 1glo
1glo + 2glox + glox = 2logx

Combine like terms: 2glox + glox = 3glox
1glo + 3glox = 2logx

Solving
1glo + 3glox = 2glox

Solving for variable 'g'.

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

Add '-2glox' to each side of the equation.
1glo + 3glox + -2glox = 2glox + -2glox

Combine like terms: 3glox + -2glox = 1glox
1glo + 1glox = 2glox + -2glox

Combine like terms: 2glox + -2glox = 0
1glo + 1glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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