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Simplifying log(x + 6) = log(5x + 2) Reorder the terms: glo(6 + x) = log(5x + 2) (6 * glo + x * glo) = log(5x + 2) (6glo + glox) = log(5x + 2) Reorder the terms: 6glo + glox = glo(2 + 5x) 6glo + glox = (2 * glo + 5x * glo) 6glo + glox = (2glo + 5glox) Solving 6glo + glox = 2glo + 5glox 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. 6glo + -2glo + glox = 2glo + -2glo + 5glox Combine like terms: 6glo + -2glo = 4glo 4glo + glox = 2glo + -2glo + 5glox Combine like terms: 2glo + -2glo = 0 4glo + glox = 0 + 5glox 4glo + glox = 5glox Add '-5glox' to each side of the equation. 4glo + glox + -5glox = 5glox + -5glox Combine like terms: glox + -5glox = -4glox 4glo + -4glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 4glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(1 + -1x) = 0 Ignore the factor 4.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 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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