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Simplifying log(6x + 1) = log(x + -5) Reorder the terms: glo(1 + 6x) = log(x + -5) (1 * glo + 6x * glo) = log(x + -5) (1glo + 6glox) = log(x + -5) Reorder the terms: 1glo + 6glox = glo(-5 + x) 1glo + 6glox = (-5 * glo + x * glo) 1glo + 6glox = (-5glo + glox) Solving 1glo + 6glox = -5glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '5glo' to each side of the equation. 1glo + 5glo + 6glox = -5glo + 5glo + glox Combine like terms: 1glo + 5glo = 6glo 6glo + 6glox = -5glo + 5glo + glox Combine like terms: -5glo + 5glo = 0 6glo + 6glox = 0 + glox 6glo + 6glox = glox Add '-1glox' to each side of the equation. 6glo + 6glox + -1glox = glox + -1glox Combine like terms: 6glox + -1glox = 5glox 6glo + 5glox = glox + -1glox Combine like terms: glox + -1glox = 0 6glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(6 + 5x) = 0Subproblem 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 '(6 + 5x)' equal to zero and attempt to solve: Simplifying 6 + 5x = 0 Solving 6 + 5x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5x = 0 + -6 5x = 0 + -6 Combine like terms: 0 + -6 = -6 5x = -6 Add '-5x' to each side of the equation. 5x + -5x = -6 + -5x Combine like terms: 5x + -5x = 0 0 = -6 + -5x Simplifying 0 = -6 + -5x 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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