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