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Simplifying Log(3x + 4) = log(2x + 5) Reorder the terms: goL(4 + 3x) = log(2x + 5) (4 * goL + 3x * goL) = log(2x + 5) (4goL + 3goxL) = log(2x + 5) Reorder the terms: 4goL + 3goxL = glo(5 + 2x) 4goL + 3goxL = (5 * glo + 2x * glo) 4goL + 3goxL = (5glo + 2glox) Solving 4goL + 3goxL = 5glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5glo' to each side of the equation. 4goL + -5glo + 3goxL = 5glo + -5glo + 2glox Reorder the terms: -5glo + 4goL + 3goxL = 5glo + -5glo + 2glox Combine like terms: 5glo + -5glo = 0 -5glo + 4goL + 3goxL = 0 + 2glox -5glo + 4goL + 3goxL = 2glox Add '-2glox' to each side of the equation. -5glo + 4goL + -2glox + 3goxL = 2glox + -2glox Reorder the terms: -5glo + -2glox + 4goL + 3goxL = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -5glo + -2glox + 4goL + 3goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-5l + -2lx + 4L + 3xL) = 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 '(-5l + -2lx + 4L + 3xL)' equal to zero and attempt to solve: Simplifying -5l + -2lx + 4L + 3xL = 0 Reorder the terms: 4L + -5l + -2lx + 3xL = 0 Solving 4L + -5l + -2lx + 3xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-4L' to each side of the equation. 4L + -5l + -2lx + -4L + 3xL = 0 + -4L Reorder the terms: 4L + -4L + -5l + -2lx + 3xL = 0 + -4L Combine like terms: 4L + -4L = 0 0 + -5l + -2lx + 3xL = 0 + -4L -5l + -2lx + 3xL = 0 + -4L Remove the zero: -5l + -2lx + 3xL = -4L Add '5l' to each side of the equation. -5l + -2lx + 5l + 3xL = -4L + 5l Reorder the terms: -5l + 5l + -2lx + 3xL = -4L + 5l Combine like terms: -5l + 5l = 0 0 + -2lx + 3xL = -4L + 5l -2lx + 3xL = -4L + 5l Add '2lx' to each side of the equation. -2lx + 2lx + 3xL = -4L + 5l + 2lx Combine like terms: -2lx + 2lx = 0 0 + 3xL = -4L + 5l + 2lx 3xL = -4L + 5l + 2lx Add '-3xL' to each side of the equation. 3xL + -3xL = -4L + 5l + 2lx + -3xL Combine like terms: 3xL + -3xL = 0 0 = -4L + 5l + 2lx + -3xL Simplifying 0 = -4L + 5l + 2lx + -3xL 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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