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Simplifying log(12) + -1log(5x2) = log(x + 3) + log(x + 2) Reorder the terms for easier multiplication: 12glo + -1log(5x2) = log(x + 3) + log(x + 2) Remove parenthesis around (5x2) 12glo + -1glo * 5x2 = log(x + 3) + log(x + 2) Reorder the terms for easier multiplication: 12glo + -1 * 5glo * x2 = log(x + 3) + log(x + 2) Multiply -1 * 5 12glo + -5glo * x2 = log(x + 3) + log(x + 2) Multiply glo * x2 12glo + -5glox2 = log(x + 3) + log(x + 2) Reorder the terms: 12glo + -5glox2 = glo(3 + x) + log(x + 2) 12glo + -5glox2 = (3 * glo + x * glo) + log(x + 2) 12glo + -5glox2 = (3glo + glox) + log(x + 2) Reorder the terms: 12glo + -5glox2 = 3glo + glox + glo(2 + x) 12glo + -5glox2 = 3glo + glox + (2 * glo + x * glo) 12glo + -5glox2 = 3glo + glox + (2glo + glox) Reorder the terms: 12glo + -5glox2 = 3glo + 2glo + glox + glox Combine like terms: 3glo + 2glo = 5glo 12glo + -5glox2 = 5glo + glox + glox Combine like terms: glox + glox = 2glox 12glo + -5glox2 = 5glo + 2glox Solving 12glo + -5glox2 = 5glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5glo' to each side of the equation. 12glo + -5glo + -5glox2 = 5glo + -5glo + 2glox Combine like terms: 12glo + -5glo = 7glo 7glo + -5glox2 = 5glo + -5glo + 2glox Combine like terms: 5glo + -5glo = 0 7glo + -5glox2 = 0 + 2glox 7glo + -5glox2 = 2glox Add '-2glox' to each side of the equation. 7glo + -2glox + -5glox2 = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 7glo + -2glox + -5glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(7 + -2x + -5x2) = 0 Factor a trinomial. glo((1 + -1x)(7 + 5x)) = 0Subproblem 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(7 + 5x)' equal to zero and attempt to solve: Simplifying 7 + 5x = 0 Solving 7 + 5x = 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 + 5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5x = 0 + -7 5x = 0 + -7 Combine like terms: 0 + -7 = -7 5x = -7 Add '-5x' to each side of the equation. 5x + -5x = -7 + -5x Combine like terms: 5x + -5x = 0 0 = -7 + -5x Simplifying 0 = -7 + -5x 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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