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Simplifying log(4x) = log(3) + log(x + -2) Remove parenthesis around (4x) glo * 4x = log(3) + log(x + -2) Reorder the terms for easier multiplication: 4glo * x = log(3) + log(x + -2) Multiply glo * x 4glox = log(3) + log(x + -2) Reorder the terms for easier multiplication: 4glox = 3glo + log(x + -2) Reorder the terms: 4glox = 3glo + glo(-2 + x) 4glox = 3glo + (-2 * glo + x * glo) 4glox = 3glo + (-2glo + glox) Combine like terms: 3glo + -2glo = 1glo 4glox = 1glo + glox Solving 4glox = 1glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1glo' to each side of the equation. -1glo + 4glox = 1glo + -1glo + glox Combine like terms: 1glo + -1glo = 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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