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Simplifying log[5](7x) = log[5](4x + 12) Remove parenthesis around (7x) glo * 5 * 7x = log[5](4x + 12) Reorder the terms for easier multiplication: 5 * 7glo * x = log[5](4x + 12) Multiply 5 * 7 35glo * x = log[5](4x + 12) Multiply glo * x 35glox = log[5](4x + 12) Reorder the terms: 35glox = glo * 5(12 + 4x) Reorder the terms for easier multiplication: 35glox = 5glo(12 + 4x) 35glox = (12 * 5glo + 4x * 5glo) 35glox = (60glo + 20glox) Solving 35glox = 60glo + 20glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-60glo' to each side of the equation. -60glo + 35glox = 60glo + -60glo + 20glox Combine like terms: 60glo + -60glo = 0 -60glo + 35glox = 0 + 20glox -60glo + 35glox = 20glox Add '-20glox' to each side of the equation. -60glo + 35glox + -20glox = 20glox + -20glox Combine like terms: 35glox + -20glox = 15glox -60glo + 15glox = 20glox + -20glox Combine like terms: 20glox + -20glox = 0 -60glo + 15glox = 0 Factor out the Greatest Common Factor (GCF), '15glo'. 15glo(-4 + x) = 0 Ignore the factor 15.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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -1x 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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