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Simplifying logx + log(x + 7) = log(13x) Reorder the terms: glox + glo(7 + x) = log(13x) glox + (7 * glo + x * glo) = log(13x) glox + (7glo + glox) = log(13x) Reorder the terms: 7glo + glox + glox = log(13x) Combine like terms: glox + glox = 2glox 7glo + 2glox = log(13x) Remove parenthesis around (13x) 7glo + 2glox = glo * 13x Reorder the terms for easier multiplication: 7glo + 2glox = 13glo * x Multiply glo * x 7glo + 2glox = 13glox Solving 7glo + 2glox = 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. 7glo + 2glox + -13glox = 13glox + -13glox Combine like terms: 2glox + -13glox = -11glox 7glo + -11glox = 13glox + -13glox Combine like terms: 13glox + -13glox = 0 7glo + -11glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(7 + -11x) = 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 '(7 + -11x)' equal to zero and attempt to solve: Simplifying 7 + -11x = 0 Solving 7 + -11x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -11x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -11x = 0 + -7 -11x = 0 + -7 Combine like terms: 0 + -7 = -7 -11x = -7 Add '11x' to each side of the equation. -11x + 11x = -7 + 11x Combine like terms: -11x + 11x = 0 0 = -7 + 11x Simplifying 0 = -7 + 11x 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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