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Simplifying Log(2x + -3) = log(x + 4) Reorder the terms: goL(-3 + 2x) = log(x + 4) (-3 * goL + 2x * goL) = log(x + 4) (-3goL + 2goxL) = log(x + 4) Reorder the terms: -3goL + 2goxL = glo(4 + x) -3goL + 2goxL = (4 * glo + x * glo) -3goL + 2goxL = (4glo + glox) Solving -3goL + 2goxL = 4glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4glo' to each side of the equation. -3goL + -4glo + 2goxL = 4glo + -4glo + glox Reorder the terms: -4glo + -3goL + 2goxL = 4glo + -4glo + glox Combine like terms: 4glo + -4glo = 0 -4glo + -3goL + 2goxL = 0 + glox -4glo + -3goL + 2goxL = glox Add '-1glox' to each side of the equation. -4glo + -3goL + -1glox + 2goxL = glox + -1glox Reorder the terms: -4glo + -1glox + -3goL + 2goxL = glox + -1glox Combine like terms: glox + -1glox = 0 -4glo + -1glox + -3goL + 2goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-4l + -1lx + -3L + 2xL) = 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 '(-4l + -1lx + -3L + 2xL)' equal to zero and attempt to solve: Simplifying -4l + -1lx + -3L + 2xL = 0 Reorder the terms: -3L + -4l + -1lx + 2xL = 0 Solving -3L + -4l + -1lx + 2xL = 0 Move all terms containing g to the left, all other terms to the right. Add '3L' to each side of the equation. -3L + -4l + -1lx + 3L + 2xL = 0 + 3L Reorder the terms: -3L + 3L + -4l + -1lx + 2xL = 0 + 3L Combine like terms: -3L + 3L = 0 0 + -4l + -1lx + 2xL = 0 + 3L -4l + -1lx + 2xL = 0 + 3L Remove the zero: -4l + -1lx + 2xL = 3L Add '4l' to each side of the equation. -4l + -1lx + 4l + 2xL = 3L + 4l Reorder the terms: -4l + 4l + -1lx + 2xL = 3L + 4l Combine like terms: -4l + 4l = 0 0 + -1lx + 2xL = 3L + 4l -1lx + 2xL = 3L + 4l Add 'lx' to each side of the equation. -1lx + lx + 2xL = 3L + 4l + lx Combine like terms: -1lx + lx = 0 0 + 2xL = 3L + 4l + lx 2xL = 3L + 4l + lx Add '-2xL' to each side of the equation. 2xL + -2xL = 3L + 4l + lx + -2xL Combine like terms: 2xL + -2xL = 0 0 = 3L + 4l + lx + -2xL Simplifying 0 = 3L + 4l + lx + -2xL 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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