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Simplifying log(2)(3x + 1) = log(2)(5x + -7) Reorder the terms: glo * 2(1 + 3x) = log(2)(5x + -7) Reorder the terms for easier multiplication: 2glo(1 + 3x) = log(2)(5x + -7) (1 * 2glo + 3x * 2glo) = log(2)(5x + -7) (2glo + 6glox) = log(2)(5x + -7) Reorder the terms: 2glo + 6glox = glo * 2(-7 + 5x) Reorder the terms for easier multiplication: 2glo + 6glox = 2glo(-7 + 5x) 2glo + 6glox = (-7 * 2glo + 5x * 2glo) 2glo + 6glox = (-14glo + 10glox) Solving 2glo + 6glox = -14glo + 10glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '14glo' to each side of the equation. 2glo + 14glo + 6glox = -14glo + 14glo + 10glox Combine like terms: 2glo + 14glo = 16glo 16glo + 6glox = -14glo + 14glo + 10glox Combine like terms: -14glo + 14glo = 0 16glo + 6glox = 0 + 10glox 16glo + 6glox = 10glox Add '-10glox' to each side of the equation. 16glo + 6glox + -10glox = 10glox + -10glox Combine like terms: 6glox + -10glox = -4glox 16glo + -4glox = 10glox + -10glox Combine like terms: 10glox + -10glox = 0 16glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(4 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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