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Simplifying Log(3x + -5) = log(4x + 7) Reorder the terms: goL(-5 + 3x) = log(4x + 7) (-5 * goL + 3x * goL) = log(4x + 7) (-5goL + 3goxL) = log(4x + 7) Reorder the terms: -5goL + 3goxL = glo(7 + 4x) -5goL + 3goxL = (7 * glo + 4x * glo) -5goL + 3goxL = (7glo + 4glox) Solving -5goL + 3goxL = 7glo + 4glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7glo' to each side of the equation. -5goL + -7glo + 3goxL = 7glo + -7glo + 4glox Reorder the terms: -7glo + -5goL + 3goxL = 7glo + -7glo + 4glox Combine like terms: 7glo + -7glo = 0 -7glo + -5goL + 3goxL = 0 + 4glox -7glo + -5goL + 3goxL = 4glox Add '-4glox' to each side of the equation. -7glo + -5goL + -4glox + 3goxL = 4glox + -4glox Reorder the terms: -7glo + -4glox + -5goL + 3goxL = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -7glo + -4glox + -5goL + 3goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-7l + -4lx + -5L + 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 '(-7l + -4lx + -5L + 3xL)' equal to zero and attempt to solve: Simplifying -7l + -4lx + -5L + 3xL = 0 Reorder the terms: -5L + -7l + -4lx + 3xL = 0 Solving -5L + -7l + -4lx + 3xL = 0 Move all terms containing g to the left, all other terms to the right. Add '5L' to each side of the equation. -5L + -7l + -4lx + 5L + 3xL = 0 + 5L Reorder the terms: -5L + 5L + -7l + -4lx + 3xL = 0 + 5L Combine like terms: -5L + 5L = 0 0 + -7l + -4lx + 3xL = 0 + 5L -7l + -4lx + 3xL = 0 + 5L Remove the zero: -7l + -4lx + 3xL = 5L Add '7l' to each side of the equation. -7l + -4lx + 7l + 3xL = 5L + 7l Reorder the terms: -7l + 7l + -4lx + 3xL = 5L + 7l Combine like terms: -7l + 7l = 0 0 + -4lx + 3xL = 5L + 7l -4lx + 3xL = 5L + 7l Add '4lx' to each side of the equation. -4lx + 4lx + 3xL = 5L + 7l + 4lx Combine like terms: -4lx + 4lx = 0 0 + 3xL = 5L + 7l + 4lx 3xL = 5L + 7l + 4lx Add '-3xL' to each side of the equation. 3xL + -3xL = 5L + 7l + 4lx + -3xL Combine like terms: 3xL + -3xL = 0 0 = 5L + 7l + 4lx + -3xL Simplifying 0 = 5L + 7l + 4lx + -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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