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Simplifying log(5) + 2log(x) = log(15x + 50) Reorder the terms for easier multiplication: 5glo + 2log(x) = log(15x + 50) Multiply glo * x 5glo + 2glox = log(15x + 50) Reorder the terms: 5glo + 2glox = glo(50 + 15x) 5glo + 2glox = (50 * glo + 15x * glo) 5glo + 2glox = (50glo + 15glox) Solving 5glo + 2glox = 50glo + 15glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-50glo' to each side of the equation. 5glo + -50glo + 2glox = 50glo + -50glo + 15glox Combine like terms: 5glo + -50glo = -45glo -45glo + 2glox = 50glo + -50glo + 15glox Combine like terms: 50glo + -50glo = 0 -45glo + 2glox = 0 + 15glox -45glo + 2glox = 15glox Add '-15glox' to each side of the equation. -45glo + 2glox + -15glox = 15glox + -15glox Combine like terms: 2glox + -15glox = -13glox -45glo + -13glox = 15glox + -15glox Combine like terms: 15glox + -15glox = 0 -45glo + -13glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(45 + 13x) = 0 Ignore the factor -1.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 '(45 + 13x)' equal to zero and attempt to solve: Simplifying 45 + 13x = 0 Solving 45 + 13x = 0 Move all terms containing g to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + 13x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 13x = 0 + -45 13x = 0 + -45 Combine like terms: 0 + -45 = -45 13x = -45 Add '-13x' to each side of the equation. 13x + -13x = -45 + -13x Combine like terms: 13x + -13x = 0 0 = -45 + -13x Simplifying 0 = -45 + -13x 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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