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Simplifying log(x + 13) + -1log(2) = log(2x + 3) Reorder the terms: glo(13 + x) + -1log(2) = log(2x + 3) (13 * glo + x * glo) + -1log(2) = log(2x + 3) (13glo + glox) + -1log(2) = log(2x + 3) Reorder the terms for easier multiplication: 13glo + glox + -1 * 2glo = log(2x + 3) Multiply -1 * 2 13glo + glox + -2glo = log(2x + 3) Reorder the terms: 13glo + -2glo + glox = log(2x + 3) Combine like terms: 13glo + -2glo = 11glo 11glo + glox = log(2x + 3) Reorder the terms: 11glo + glox = glo(3 + 2x) 11glo + glox = (3 * glo + 2x * glo) 11glo + glox = (3glo + 2glox) Solving 11glo + glox = 3glo + 2glox 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. 11glo + -3glo + glox = 3glo + -3glo + 2glox Combine like terms: 11glo + -3glo = 8glo 8glo + glox = 3glo + -3glo + 2glox Combine like terms: 3glo + -3glo = 0 8glo + glox = 0 + 2glox 8glo + glox = 2glox Add '-2glox' to each side of the equation. 8glo + glox + -2glox = 2glox + -2glox Combine like terms: glox + -2glox = -1glox 8glo + -1glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 8glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + 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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