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Simplifying Log(x + 3) = log(6 + 4x) Reorder the terms: goL(3 + x) = log(6 + 4x) (3 * goL + x * goL) = log(6 + 4x) (3goL + goxL) = log(6 + 4x) 3goL + goxL = (6 * glo + 4x * glo) 3goL + goxL = (6glo + 4glox) Solving 3goL + goxL = 6glo + 4glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6glo' to each side of the equation. 3goL + -6glo + goxL = 6glo + -6glo + 4glox Reorder the terms: -6glo + 3goL + goxL = 6glo + -6glo + 4glox Combine like terms: 6glo + -6glo = 0 -6glo + 3goL + goxL = 0 + 4glox -6glo + 3goL + goxL = 4glox Add '-4glox' to each side of the equation. -6glo + 3goL + -4glox + goxL = 4glox + -4glox Reorder the terms: -6glo + -4glox + 3goL + goxL = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -6glo + -4glox + 3goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-6l + -4lx + 3L + 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 '(-6l + -4lx + 3L + xL)' equal to zero and attempt to solve: Simplifying -6l + -4lx + 3L + xL = 0 Reorder the terms: 3L + -6l + -4lx + xL = 0 Solving 3L + -6l + -4lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-3L' to each side of the equation. 3L + -6l + -4lx + -3L + xL = 0 + -3L Reorder the terms: 3L + -3L + -6l + -4lx + xL = 0 + -3L Combine like terms: 3L + -3L = 0 0 + -6l + -4lx + xL = 0 + -3L -6l + -4lx + xL = 0 + -3L Remove the zero: -6l + -4lx + xL = -3L Add '6l' to each side of the equation. -6l + -4lx + 6l + xL = -3L + 6l Reorder the terms: -6l + 6l + -4lx + xL = -3L + 6l Combine like terms: -6l + 6l = 0 0 + -4lx + xL = -3L + 6l -4lx + xL = -3L + 6l Add '4lx' to each side of the equation. -4lx + 4lx + xL = -3L + 6l + 4lx Combine like terms: -4lx + 4lx = 0 0 + xL = -3L + 6l + 4lx xL = -3L + 6l + 4lx Add '-1xL' to each side of the equation. xL + -1xL = -3L + 6l + 4lx + -1xL Combine like terms: xL + -1xL = 0 0 = -3L + 6l + 4lx + -1xL Simplifying 0 = -3L + 6l + 4lx + -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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