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Simplifying log[5](x + 18) = log[5](6 + -1x) Reorder the terms: glo * 5(18 + x) = log[5](6 + -1x) Reorder the terms for easier multiplication: 5glo(18 + x) = log[5](6 + -1x) (18 * 5glo + x * 5glo) = log[5](6 + -1x) (90glo + 5glox) = log[5](6 + -1x) Reorder the terms for easier multiplication: 90glo + 5glox = 5glo(6 + -1x) 90glo + 5glox = (6 * 5glo + -1x * 5glo) 90glo + 5glox = (30glo + -5glox) Solving 90glo + 5glox = 30glo + -5glox 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. 90glo + -30glo + 5glox = 30glo + -30glo + -5glox Combine like terms: 90glo + -30glo = 60glo 60glo + 5glox = 30glo + -30glo + -5glox Combine like terms: 30glo + -30glo = 0 60glo + 5glox = 0 + -5glox 60glo + 5glox = -5glox Add '5glox' to each side of the equation. 60glo + 5glox + 5glox = -5glox + 5glox Combine like terms: 5glox + 5glox = 10glox 60glo + 10glox = -5glox + 5glox Combine like terms: -5glox + 5glox = 0 60glo + 10glox = 0 Factor out the Greatest Common Factor (GCF), '10glo'. 10glo(6 + x) = 0 Ignore the factor 10.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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -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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