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Simplifying log(6x + -1) = log(2x + 15) Reorder the terms: glo(-1 + 6x) = log(2x + 15) (-1 * glo + 6x * glo) = log(2x + 15) (-1glo + 6glox) = log(2x + 15) Reorder the terms: -1glo + 6glox = glo(15 + 2x) -1glo + 6glox = (15 * glo + 2x * glo) -1glo + 6glox = (15glo + 2glox) Solving -1glo + 6glox = 15glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-15glo' to each side of the equation. -1glo + -15glo + 6glox = 15glo + -15glo + 2glox Combine like terms: -1glo + -15glo = -16glo -16glo + 6glox = 15glo + -15glo + 2glox Combine like terms: 15glo + -15glo = 0 -16glo + 6glox = 0 + 2glox -16glo + 6glox = 2glox Add '-2glox' to each side of the equation. -16glo + 6glox + -2glox = 2glox + -2glox Combine like terms: 6glox + -2glox = 4glox -16glo + 4glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -16glo + 4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(-4 + x) = 0 Ignore the factor 4.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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