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Simplifying log(7x + 1) = log(x + -2) Reorder the terms: glo(1 + 7x) = log(x + -2) (1 * glo + 7x * glo) = log(x + -2) (1glo + 7glox) = log(x + -2) Reorder the terms: 1glo + 7glox = glo(-2 + x) 1glo + 7glox = (-2 * glo + x * glo) 1glo + 7glox = (-2glo + glox) Solving 1glo + 7glox = -2glo + glox 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. 1glo + 2glo + 7glox = -2glo + 2glo + glox Combine like terms: 1glo + 2glo = 3glo 3glo + 7glox = -2glo + 2glo + glox Combine like terms: -2glo + 2glo = 0 3glo + 7glox = 0 + glox 3glo + 7glox = glox Add '-1glox' to each side of the equation. 3glo + 7glox + -1glox = glox + -1glox Combine like terms: 7glox + -1glox = 6glox 3glo + 6glox = glox + -1glox Combine like terms: glox + -1glox = 0 3glo + 6glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(1 + 2x) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -2x 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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