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Simplifying Log(5)(7x + -2) = log(5)(3x + 6) Reorder the terms: goL * 5(-2 + 7x) = log(5)(3x + 6) Reorder the terms for easier multiplication: 5goL(-2 + 7x) = log(5)(3x + 6) (-2 * 5goL + 7x * 5goL) = log(5)(3x + 6) (-10goL + 35goxL) = log(5)(3x + 6) Reorder the terms: -10goL + 35goxL = glo * 5(6 + 3x) Reorder the terms for easier multiplication: -10goL + 35goxL = 5glo(6 + 3x) -10goL + 35goxL = (6 * 5glo + 3x * 5glo) -10goL + 35goxL = (30glo + 15glox) Solving -10goL + 35goxL = 30glo + 15glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-30glo' to each side of the equation. -10goL + -30glo + 35goxL = 30glo + -30glo + 15glox Reorder the terms: -30glo + -10goL + 35goxL = 30glo + -30glo + 15glox Combine like terms: 30glo + -30glo = 0 -30glo + -10goL + 35goxL = 0 + 15glox -30glo + -10goL + 35goxL = 15glox Add '-15glox' to each side of the equation. -30glo + -10goL + -15glox + 35goxL = 15glox + -15glox Reorder the terms: -30glo + -15glox + -10goL + 35goxL = 15glox + -15glox Combine like terms: 15glox + -15glox = 0 -30glo + -15glox + -10goL + 35goxL = 0 Factor out the Greatest Common Factor (GCF), '5go'. 5go(-6l + -3lx + -2L + 7xL) = 0 Ignore the factor 5.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 '(-6l + -3lx + -2L + 7xL)' equal to zero and attempt to solve: Simplifying -6l + -3lx + -2L + 7xL = 0 Reorder the terms: -2L + -6l + -3lx + 7xL = 0 Solving -2L + -6l + -3lx + 7xL = 0 Move all terms containing g to the left, all other terms to the right. Add '2L' to each side of the equation. -2L + -6l + -3lx + 2L + 7xL = 0 + 2L Reorder the terms: -2L + 2L + -6l + -3lx + 7xL = 0 + 2L Combine like terms: -2L + 2L = 0 0 + -6l + -3lx + 7xL = 0 + 2L -6l + -3lx + 7xL = 0 + 2L Remove the zero: -6l + -3lx + 7xL = 2L Add '6l' to each side of the equation. -6l + -3lx + 6l + 7xL = 2L + 6l Reorder the terms: -6l + 6l + -3lx + 7xL = 2L + 6l Combine like terms: -6l + 6l = 0 0 + -3lx + 7xL = 2L + 6l -3lx + 7xL = 2L + 6l Add '3lx' to each side of the equation. -3lx + 3lx + 7xL = 2L + 6l + 3lx Combine like terms: -3lx + 3lx = 0 0 + 7xL = 2L + 6l + 3lx 7xL = 2L + 6l + 3lx Add '-7xL' to each side of the equation. 7xL + -7xL = 2L + 6l + 3lx + -7xL Combine like terms: 7xL + -7xL = 0 0 = 2L + 6l + 3lx + -7xL Simplifying 0 = 2L + 6l + 3lx + -7xL 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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