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Simplifying log(x + 15) = log(x + 3) + logx Reorder the terms: glo(15 + x) = log(x + 3) + logx (15 * glo + x * glo) = log(x + 3) + logx (15glo + glox) = log(x + 3) + logx Reorder the terms: 15glo + glox = glo(3 + x) + logx 15glo + glox = (3 * glo + x * glo) + logx 15glo + glox = (3glo + glox) + logx Combine like terms: glox + glox = 2glox 15glo + glox = 3glo + 2glox Solving 15glo + 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. 15glo + -3glo + glox = 3glo + -3glo + 2glox Combine like terms: 15glo + -3glo = 12glo 12glo + glox = 3glo + -3glo + 2glox Combine like terms: 3glo + -3glo = 0 12glo + glox = 0 + 2glox 12glo + glox = 2glox Add '-2glox' to each side of the equation. 12glo + glox + -2glox = 2glox + -2glox Combine like terms: glox + -2glox = -1glox 12glo + -1glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 12glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(12 + -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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Add 'x' to each side of the equation. -1x + x = -12 + x Combine like terms: -1x + x = 0 0 = -12 + x Simplifying 0 = -12 + 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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