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Simplifying log(7x + 1) = log(6x + 2) Reorder the terms: glo(1 + 7x) = log(6x + 2) (1 * glo + 7x * glo) = log(6x + 2) (1glo + 7glox) = log(6x + 2) Reorder the terms: 1glo + 7glox = glo(2 + 6x) 1glo + 7glox = (2 * glo + 6x * glo) 1glo + 7glox = (2glo + 6glox) Solving 1glo + 7glox = 2glo + 6glox 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 + 6glox Combine like terms: 1glo + -2glo = -1glo -1glo + 7glox = 2glo + -2glo + 6glox Combine like terms: 2glo + -2glo = 0 -1glo + 7glox = 0 + 6glox -1glo + 7glox = 6glox Add '-6glox' to each side of the equation. -1glo + 7glox + -6glox = 6glox + -6glox Combine like terms: 7glox + -6glox = 1glox -1glo + 1glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 -1glo + 1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-1 + x) = 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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -1x 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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