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Simplifying log(x) + log(-4x + -23) = log(15) Multiply glo * x glox + log(-4x + -23) = log(15) Reorder the terms: glox + glo(-23 + -4x) = log(15) glox + (-23 * glo + -4x * glo) = log(15) glox + (-23glo + -4glox) = log(15) Reorder the terms: -23glo + glox + -4glox = log(15) Combine like terms: glox + -4glox = -3glox -23glo + -3glox = log(15) Reorder the terms for easier multiplication: -23glo + -3glox = 15glo Solving -23glo + -3glox = 15glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-15glo' to each side of the equation. -23glo + -15glo + -3glox = 15glo + -15glo Combine like terms: -23glo + -15glo = -38glo -38glo + -3glox = 15glo + -15glo Combine like terms: 15glo + -15glo = 0 -38glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(38 + 3x) = 0 Ignore the factor -1.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 '(38 + 3x)' equal to zero and attempt to solve: Simplifying 38 + 3x = 0 Solving 38 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + 3x = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 3x = 0 + -38 3x = 0 + -38 Combine like terms: 0 + -38 = -38 3x = -38 Add '-3x' to each side of the equation. 3x + -3x = -38 + -3x Combine like terms: 3x + -3x = 0 0 = -38 + -3x Simplifying 0 = -38 + -3x 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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