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Simplifying log(x + 2) = 1 + log(4x + 3) Reorder the terms: glo(2 + x) = 1 + log(4x + 3) (2 * glo + x * glo) = 1 + log(4x + 3) (2glo + glox) = 1 + log(4x + 3) Reorder the terms: 2glo + glox = 1 + glo(3 + 4x) 2glo + glox = 1 + (3 * glo + 4x * glo) 2glo + glox = 1 + (3glo + 4glox) Solving 2glo + glox = 1 + 3glo + 4glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3glo' to each side of the equation. 2glo + -3glo + glox = 1 + 3glo + -3glo + 4glox Combine like terms: 2glo + -3glo = -1glo -1glo + glox = 1 + 3glo + -3glo + 4glox Combine like terms: 3glo + -3glo = 0 -1glo + glox = 1 + 0 + 4glox -1glo + glox = 1 + 4glox Add '-4glox' to each side of the equation. -1glo + glox + -4glox = 1 + 4glox + -4glox Combine like terms: glox + -4glox = -3glox -1glo + -3glox = 1 + 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -1glo + -3glox = 1 + 0 -1glo + -3glox = 1 Reorder the terms: -1 + -1glo + -3glox = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -1glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + glo + 3glox) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + glo + 3glox)' equal to zero and attempt to solve: Simplifying 1 + glo + 3glox = 0 Solving 1 + glo + 3glox = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + glo + -1 + 3glox = 0 + -1 Reorder the terms: 1 + -1 + glo + 3glox = 0 + -1 Combine like terms: 1 + -1 = 0 0 + glo + 3glox = 0 + -1 glo + 3glox = 0 + -1 Combine like terms: 0 + -1 = -1 glo + 3glox = -1 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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