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Simplifying Log(2x + 5) = log(3x + -7) Reorder the terms: goL(5 + 2x) = log(3x + -7) (5 * goL + 2x * goL) = log(3x + -7) (5goL + 2goxL) = log(3x + -7) Reorder the terms: 5goL + 2goxL = glo(-7 + 3x) 5goL + 2goxL = (-7 * glo + 3x * glo) 5goL + 2goxL = (-7glo + 3glox) Solving 5goL + 2goxL = -7glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '7glo' to each side of the equation. 5goL + 7glo + 2goxL = -7glo + 7glo + 3glox Reorder the terms: 7glo + 5goL + 2goxL = -7glo + 7glo + 3glox Combine like terms: -7glo + 7glo = 0 7glo + 5goL + 2goxL = 0 + 3glox 7glo + 5goL + 2goxL = 3glox Add '-3glox' to each side of the equation. 7glo + 5goL + -3glox + 2goxL = 3glox + -3glox Reorder the terms: 7glo + -3glox + 5goL + 2goxL = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 7glo + -3glox + 5goL + 2goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(7l + -3lx + 5L + 2xL) = 0Subproblem 1
Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(7l + -3lx + 5L + 2xL)' equal to zero and attempt to solve: Simplifying 7l + -3lx + 5L + 2xL = 0 Reorder the terms: 5L + 7l + -3lx + 2xL = 0 Solving 5L + 7l + -3lx + 2xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-5L' to each side of the equation. 5L + 7l + -3lx + -5L + 2xL = 0 + -5L Reorder the terms: 5L + -5L + 7l + -3lx + 2xL = 0 + -5L Combine like terms: 5L + -5L = 0 0 + 7l + -3lx + 2xL = 0 + -5L 7l + -3lx + 2xL = 0 + -5L Remove the zero: 7l + -3lx + 2xL = -5L Add '-7l' to each side of the equation. 7l + -3lx + -7l + 2xL = -5L + -7l Reorder the terms: 7l + -7l + -3lx + 2xL = -5L + -7l Combine like terms: 7l + -7l = 0 0 + -3lx + 2xL = -5L + -7l -3lx + 2xL = -5L + -7l Add '3lx' to each side of the equation. -3lx + 3lx + 2xL = -5L + -7l + 3lx Combine like terms: -3lx + 3lx = 0 0 + 2xL = -5L + -7l + 3lx 2xL = -5L + -7l + 3lx Add '-2xL' to each side of the equation. 2xL + -2xL = -5L + -7l + 3lx + -2xL Combine like terms: 2xL + -2xL = 0 0 = -5L + -7l + 3lx + -2xL Simplifying 0 = -5L + -7l + 3lx + -2xL 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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