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Simplifying log(x) + log(x + 5) = log(6x + 12) Multiply glo * x glox + log(x + 5) = log(6x + 12) Reorder the terms: glox + glo(5 + x) = log(6x + 12) glox + (5 * glo + x * glo) = log(6x + 12) glox + (5glo + glox) = log(6x + 12) Reorder the terms: 5glo + glox + glox = log(6x + 12) Combine like terms: glox + glox = 2glox 5glo + 2glox = log(6x + 12) Reorder the terms: 5glo + 2glox = glo(12 + 6x) 5glo + 2glox = (12 * glo + 6x * glo) 5glo + 2glox = (12glo + 6glox) Solving 5glo + 2glox = 12glo + 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12glo' to each side of the equation. 5glo + -12glo + 2glox = 12glo + -12glo + 6glox Combine like terms: 5glo + -12glo = -7glo -7glo + 2glox = 12glo + -12glo + 6glox Combine like terms: 12glo + -12glo = 0 -7glo + 2glox = 0 + 6glox -7glo + 2glox = 6glox Add '-6glox' to each side of the equation. -7glo + 2glox + -6glox = 6glox + -6glox Combine like terms: 2glox + -6glox = -4glox -7glo + -4glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 -7glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(7 + 4x) = 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 '(7 + 4x)' equal to zero and attempt to solve: Simplifying 7 + 4x = 0 Solving 7 + 4x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4x = 0 + -7 4x = 0 + -7 Combine like terms: 0 + -7 = -7 4x = -7 Add '-4x' to each side of the equation. 4x + -4x = -7 + -4x Combine like terms: 4x + -4x = 0 0 = -7 + -4x Simplifying 0 = -7 + -4x 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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