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Simplifying log(2)(7x + 1) = log(2)(2 + x) Reorder the terms: glo * 2(1 + 7x) = log(2)(2 + x) Reorder the terms for easier multiplication: 2glo(1 + 7x) = log(2)(2 + x) (1 * 2glo + 7x * 2glo) = log(2)(2 + x) (2glo + 14glox) = log(2)(2 + x) Reorder the terms for easier multiplication: 2glo + 14glox = 2glo(2 + x) 2glo + 14glox = (2 * 2glo + x * 2glo) 2glo + 14glox = (4glo + 2glox) Solving 2glo + 14glox = 4glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4glo' to each side of the equation. 2glo + -4glo + 14glox = 4glo + -4glo + 2glox Combine like terms: 2glo + -4glo = -2glo -2glo + 14glox = 4glo + -4glo + 2glox Combine like terms: 4glo + -4glo = 0 -2glo + 14glox = 0 + 2glox -2glo + 14glox = 2glox Add '-2glox' to each side of the equation. -2glo + 14glox + -2glox = 2glox + -2glox Combine like terms: 14glox + -2glox = 12glox -2glo + 12glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -2glo + 12glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-1 + 6x) = 0 Ignore the factor 2.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 '(-1 + 6x)' equal to zero and attempt to solve: Simplifying -1 + 6x = 0 Solving -1 + 6x = 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 + 6x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6x = 0 + 1 6x = 0 + 1 Combine like terms: 0 + 1 = 1 6x = 1 Add '-6x' to each side of the equation. 6x + -6x = 1 + -6x Combine like terms: 6x + -6x = 0 0 = 1 + -6x Simplifying 0 = 1 + -6x 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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