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Simplifying log(5)(6x + 62) = log(5)(x + 12) Reorder the terms: glo * 5(62 + 6x) = log(5)(x + 12) Reorder the terms for easier multiplication: 5glo(62 + 6x) = log(5)(x + 12) (62 * 5glo + 6x * 5glo) = log(5)(x + 12) (310glo + 30glox) = log(5)(x + 12) Reorder the terms: 310glo + 30glox = glo * 5(12 + x) Reorder the terms for easier multiplication: 310glo + 30glox = 5glo(12 + x) 310glo + 30glox = (12 * 5glo + x * 5glo) 310glo + 30glox = (60glo + 5glox) Solving 310glo + 30glox = 60glo + 5glox 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. 310glo + -60glo + 30glox = 60glo + -60glo + 5glox Combine like terms: 310glo + -60glo = 250glo 250glo + 30glox = 60glo + -60glo + 5glox Combine like terms: 60glo + -60glo = 0 250glo + 30glox = 0 + 5glox 250glo + 30glox = 5glox Add '-5glox' to each side of the equation. 250glo + 30glox + -5glox = 5glox + -5glox Combine like terms: 30glox + -5glox = 25glox 250glo + 25glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 250glo + 25glox = 0 Factor out the Greatest Common Factor (GCF), '25glo'. 25glo(10 + x) = 0 Ignore the factor 25.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 '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Add '-1x' to each side of the equation. x + -1x = -10 + -1x Combine like terms: x + -1x = 0 0 = -10 + -1x Simplifying 0 = -10 + -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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