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Simplifying Log(7)(2x + 8) = log(7)(x + 5) Reorder the terms: goL * 7(8 + 2x) = log(7)(x + 5) Reorder the terms for easier multiplication: 7goL(8 + 2x) = log(7)(x + 5) (8 * 7goL + 2x * 7goL) = log(7)(x + 5) (56goL + 14goxL) = log(7)(x + 5) Reorder the terms: 56goL + 14goxL = glo * 7(5 + x) Reorder the terms for easier multiplication: 56goL + 14goxL = 7glo(5 + x) 56goL + 14goxL = (5 * 7glo + x * 7glo) 56goL + 14goxL = (35glo + 7glox) Solving 56goL + 14goxL = 35glo + 7glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-35glo' to each side of the equation. 56goL + -35glo + 14goxL = 35glo + -35glo + 7glox Reorder the terms: -35glo + 56goL + 14goxL = 35glo + -35glo + 7glox Combine like terms: 35glo + -35glo = 0 -35glo + 56goL + 14goxL = 0 + 7glox -35glo + 56goL + 14goxL = 7glox Add '-7glox' to each side of the equation. -35glo + 56goL + -7glox + 14goxL = 7glox + -7glox Reorder the terms: -35glo + -7glox + 56goL + 14goxL = 7glox + -7glox Combine like terms: 7glox + -7glox = 0 -35glo + -7glox + 56goL + 14goxL = 0 Factor out the Greatest Common Factor (GCF), '7go'. 7go(-5l + -1lx + 8L + 2xL) = 0 Ignore the factor 7.Subproblem 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 + -1lx + 8L + 2xL)' equal to zero and attempt to solve: Simplifying -5l + -1lx + 8L + 2xL = 0 Reorder the terms: 8L + -5l + -1lx + 2xL = 0 Solving 8L + -5l + -1lx + 2xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-8L' to each side of the equation. 8L + -5l + -1lx + -8L + 2xL = 0 + -8L Reorder the terms: 8L + -8L + -5l + -1lx + 2xL = 0 + -8L Combine like terms: 8L + -8L = 0 0 + -5l + -1lx + 2xL = 0 + -8L -5l + -1lx + 2xL = 0 + -8L Remove the zero: -5l + -1lx + 2xL = -8L Add '5l' to each side of the equation. -5l + -1lx + 5l + 2xL = -8L + 5l Reorder the terms: -5l + 5l + -1lx + 2xL = -8L + 5l Combine like terms: -5l + 5l = 0 0 + -1lx + 2xL = -8L + 5l -1lx + 2xL = -8L + 5l Add 'lx' to each side of the equation. -1lx + lx + 2xL = -8L + 5l + lx Combine like terms: -1lx + lx = 0 0 + 2xL = -8L + 5l + lx 2xL = -8L + 5l + lx Add '-2xL' to each side of the equation. 2xL + -2xL = -8L + 5l + lx + -2xL Combine like terms: 2xL + -2xL = 0 0 = -8L + 5l + lx + -2xL Simplifying 0 = -8L + 5l + lx + -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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