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Simplifying log(3)(2x + -10) = log(3)(14 + 4x) Reorder the terms: glo * 3(-10 + 2x) = log(3)(14 + 4x) Reorder the terms for easier multiplication: 3glo(-10 + 2x) = log(3)(14 + 4x) (-10 * 3glo + 2x * 3glo) = log(3)(14 + 4x) (-30glo + 6glox) = log(3)(14 + 4x) Reorder the terms for easier multiplication: -30glo + 6glox = 3glo(14 + 4x) -30glo + 6glox = (14 * 3glo + 4x * 3glo) -30glo + 6glox = (42glo + 12glox) Solving -30glo + 6glox = 42glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-42glo' to each side of the equation. -30glo + -42glo + 6glox = 42glo + -42glo + 12glox Combine like terms: -30glo + -42glo = -72glo -72glo + 6glox = 42glo + -42glo + 12glox Combine like terms: 42glo + -42glo = 0 -72glo + 6glox = 0 + 12glox -72glo + 6glox = 12glox Add '-12glox' to each side of the equation. -72glo + 6glox + -12glox = 12glox + -12glox Combine like terms: 6glox + -12glox = -6glox -72glo + -6glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 -72glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '-6glo'. -6glo(12 + x) = 0 Ignore the factor -6.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 '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Add '-1x' to each side of the equation. x + -1x = -12 + -1x Combine like terms: x + -1x = 0 0 = -12 + -1x Simplifying 0 = -12 + -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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