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Simplifying log(x + 14) + -1log(2) = log(5x + 6) Reorder the terms: glo(14 + x) + -1log(2) = log(5x + 6) (14 * glo + x * glo) + -1log(2) = log(5x + 6) (14glo + glox) + -1log(2) = log(5x + 6) Reorder the terms for easier multiplication: 14glo + glox + -1 * 2glo = log(5x + 6) Multiply -1 * 2 14glo + glox + -2glo = log(5x + 6) Reorder the terms: 14glo + -2glo + glox = log(5x + 6) Combine like terms: 14glo + -2glo = 12glo 12glo + glox = log(5x + 6) Reorder the terms: 12glo + glox = glo(6 + 5x) 12glo + glox = (6 * glo + 5x * glo) 12glo + glox = (6glo + 5glox) Solving 12glo + glox = 6glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6glo' to each side of the equation. 12glo + -6glo + glox = 6glo + -6glo + 5glox Combine like terms: 12glo + -6glo = 6glo 6glo + glox = 6glo + -6glo + 5glox Combine like terms: 6glo + -6glo = 0 6glo + glox = 0 + 5glox 6glo + glox = 5glox Add '-5glox' to each side of the equation. 6glo + glox + -5glox = 5glox + -5glox Combine like terms: glox + -5glox = -4glox 6glo + -4glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 6glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(3 + -2x) = 0 Ignore the factor 2.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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Add '2x' to each side of the equation. -2x + 2x = -3 + 2x Combine like terms: -2x + 2x = 0 0 = -3 + 2x Simplifying 0 = -3 + 2x 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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