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Simplifying Log(x + 1) + log(4x + -3) = log(2 + -7x) Reorder the terms: goL(1 + x) + log(4x + -3) = log(2 + -7x) (1 * goL + x * goL) + log(4x + -3) = log(2 + -7x) (1goL + goxL) + log(4x + -3) = log(2 + -7x) Reorder the terms: 1goL + goxL + glo(-3 + 4x) = log(2 + -7x) 1goL + goxL + (-3 * glo + 4x * glo) = log(2 + -7x) 1goL + goxL + (-3glo + 4glox) = log(2 + -7x) Reorder the terms: -3glo + 4glox + 1goL + goxL = log(2 + -7x) -3glo + 4glox + 1goL + goxL = (2 * glo + -7x * glo) -3glo + 4glox + 1goL + goxL = (2glo + -7glox) Solving -3glo + 4glox + 1goL + goxL = 2glo + -7glox 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. -3glo + 4glox + 1goL + -2glo + goxL = 2glo + -2glo + -7glox Reorder the terms: -3glo + -2glo + 4glox + 1goL + goxL = 2glo + -2glo + -7glox Combine like terms: -3glo + -2glo = -5glo -5glo + 4glox + 1goL + goxL = 2glo + -2glo + -7glox Combine like terms: 2glo + -2glo = 0 -5glo + 4glox + 1goL + goxL = 0 + -7glox -5glo + 4glox + 1goL + goxL = -7glox Add '7glox' to each side of the equation. -5glo + 4glox + 1goL + 7glox + goxL = -7glox + 7glox Reorder the terms: -5glo + 4glox + 7glox + 1goL + goxL = -7glox + 7glox Combine like terms: 4glox + 7glox = 11glox -5glo + 11glox + 1goL + goxL = -7glox + 7glox Combine like terms: -7glox + 7glox = 0 -5glo + 11glox + 1goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-5l + 11lx + L + 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 '(-5l + 11lx + L + xL)' equal to zero and attempt to solve: Simplifying -5l + 11lx + L + xL = 0 Reorder the terms: L + -5l + 11lx + xL = 0 Solving L + -5l + 11lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-1L' to each side of the equation. L + -5l + 11lx + -1L + xL = 0 + -1L Reorder the terms: L + -1L + -5l + 11lx + xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -5l + 11lx + xL = 0 + -1L -5l + 11lx + xL = 0 + -1L Remove the zero: -5l + 11lx + xL = -1L Add '5l' to each side of the equation. -5l + 11lx + 5l + xL = -1L + 5l Reorder the terms: -5l + 5l + 11lx + xL = -1L + 5l Combine like terms: -5l + 5l = 0 0 + 11lx + xL = -1L + 5l 11lx + xL = -1L + 5l Add '-11lx' to each side of the equation. 11lx + -11lx + xL = -1L + 5l + -11lx Combine like terms: 11lx + -11lx = 0 0 + xL = -1L + 5l + -11lx xL = -1L + 5l + -11lx Add '-1xL' to each side of the equation. xL + -1xL = -1L + 5l + -11lx + -1xL Combine like terms: xL + -1xL = 0 0 = -1L + 5l + -11lx + -1xL Simplifying 0 = -1L + 5l + -11lx + -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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