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