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