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