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Simplifying log(4x + 1) = log(x + 2) Reorder the terms: glo(1 + 4x) = log(x + 2) (1 * glo + 4x * glo) = log(x + 2) (1glo + 4glox) = log(x + 2) Reorder the terms: 1glo + 4glox = glo(2 + x) 1glo + 4glox = (2 * glo + x * glo) 1glo + 4glox = (2glo + glox) Solving 1glo + 4glox = 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 + 4glox = 2glo + -2glo + glox Combine like terms: 1glo + -2glo = -1glo -1glo + 4glox = 2glo + -2glo + glox Combine like terms: 2glo + -2glo = 0 -1glo + 4glox = 0 + glox -1glo + 4glox = glox Add '-1glox' to each side of the equation. -1glo + 4glox + -1glox = glox + -1glox Combine like terms: 4glox + -1glox = 3glox -1glo + 3glox = glox + -1glox Combine like terms: glox + -1glox = 0 -1glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-1 + 3x) = 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 + 3x)' equal to zero and attempt to solve: Simplifying -1 + 3x = 0 Solving -1 + 3x = 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 + 3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3x = 0 + 1 3x = 0 + 1 Combine like terms: 0 + 1 = 1 3x = 1 Add '-3x' to each side of the equation. 3x + -3x = 1 + -3x Combine like terms: 3x + -3x = 0 0 = 1 + -3x Simplifying 0 = 1 + -3x 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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