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