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Simplifying log(3)(5x) = log(3)(x + 10) Remove parenthesis around (5x) glo * 3 * 5x = log(3)(x + 10) Reorder the terms for easier multiplication: 3 * 5glo * x = log(3)(x + 10) Multiply 3 * 5 15glo * x = log(3)(x + 10) Multiply glo * x 15glox = log(3)(x + 10) Reorder the terms: 15glox = glo * 3(10 + x) Reorder the terms for easier multiplication: 15glox = 3glo(10 + x) 15glox = (10 * 3glo + x * 3glo) 15glox = (30glo + 3glox) Solving 15glox = 30glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-30glo' to each side of the equation. -30glo + 15glox = 30glo + -30glo + 3glox Combine like terms: 30glo + -30glo = 0 -30glo + 15glox = 0 + 3glox -30glo + 15glox = 3glox Add '-3glox' to each side of the equation. -30glo + 15glox + -3glox = 3glox + -3glox Combine like terms: 15glox + -3glox = 12glox -30glo + 12glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -30glo + 12glox = 0 Factor out the Greatest Common Factor (GCF), '6glo'. 6glo(-5 + 2x) = 0 Ignore the factor 6.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 '(-5 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Add '-2x' to each side of the equation. 2x + -2x = 5 + -2x Combine like terms: 2x + -2x = 0 0 = 5 + -2x Simplifying 0 = 5 + -2x 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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