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Simplifying Log(3x + -10) = log(4x + 2) Reorder the terms: goL(-10 + 3x) = log(4x + 2) (-10 * goL + 3x * goL) = log(4x + 2) (-10goL + 3goxL) = log(4x + 2) Reorder the terms: -10goL + 3goxL = glo(2 + 4x) -10goL + 3goxL = (2 * glo + 4x * glo) -10goL + 3goxL = (2glo + 4glox) Solving -10goL + 3goxL = 2glo + 4glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glo' to each side of the equation. -10goL + -2glo + 3goxL = 2glo + -2glo + 4glox Reorder the terms: -2glo + -10goL + 3goxL = 2glo + -2glo + 4glox Combine like terms: 2glo + -2glo = 0 -2glo + -10goL + 3goxL = 0 + 4glox -2glo + -10goL + 3goxL = 4glox Add '-4glox' to each side of the equation. -2glo + -10goL + -4glox + 3goxL = 4glox + -4glox Reorder the terms: -2glo + -4glox + -10goL + 3goxL = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -2glo + -4glox + -10goL + 3goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-2l + -4lx + -10L + 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 '(-2l + -4lx + -10L + 3xL)' equal to zero and attempt to solve: Simplifying -2l + -4lx + -10L + 3xL = 0 Reorder the terms: -10L + -2l + -4lx + 3xL = 0 Solving -10L + -2l + -4lx + 3xL = 0 Move all terms containing g to the left, all other terms to the right. Add '10L' to each side of the equation. -10L + -2l + -4lx + 10L + 3xL = 0 + 10L Reorder the terms: -10L + 10L + -2l + -4lx + 3xL = 0 + 10L Combine like terms: -10L + 10L = 0 0 + -2l + -4lx + 3xL = 0 + 10L -2l + -4lx + 3xL = 0 + 10L Remove the zero: -2l + -4lx + 3xL = 10L Add '2l' to each side of the equation. -2l + -4lx + 2l + 3xL = 10L + 2l Reorder the terms: -2l + 2l + -4lx + 3xL = 10L + 2l Combine like terms: -2l + 2l = 0 0 + -4lx + 3xL = 10L + 2l -4lx + 3xL = 10L + 2l Add '4lx' to each side of the equation. -4lx + 4lx + 3xL = 10L + 2l + 4lx Combine like terms: -4lx + 4lx = 0 0 + 3xL = 10L + 2l + 4lx 3xL = 10L + 2l + 4lx Add '-3xL' to each side of the equation. 3xL + -3xL = 10L + 2l + 4lx + -3xL Combine like terms: 3xL + -3xL = 0 0 = 10L + 2l + 4lx + -3xL Simplifying 0 = 10L + 2l + 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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