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Simplifying log(x + 13) + -1log(2) = log(5x + 3) Reorder the terms: glo(13 + x) + -1log(2) = log(5x + 3) (13 * glo + x * glo) + -1log(2) = log(5x + 3) (13glo + glox) + -1log(2) = log(5x + 3) Reorder the terms for easier multiplication: 13glo + glox + -1 * 2glo = log(5x + 3) Multiply -1 * 2 13glo + glox + -2glo = log(5x + 3) Reorder the terms: 13glo + -2glo + glox = log(5x + 3) Combine like terms: 13glo + -2glo = 11glo 11glo + glox = log(5x + 3) Reorder the terms: 11glo + glox = glo(3 + 5x) 11glo + glox = (3 * glo + 5x * glo) 11glo + glox = (3glo + 5glox) Solving 11glo + glox = 3glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3glo' to each side of the equation. 11glo + -3glo + glox = 3glo + -3glo + 5glox Combine like terms: 11glo + -3glo = 8glo 8glo + glox = 3glo + -3glo + 5glox Combine like terms: 3glo + -3glo = 0 8glo + glox = 0 + 5glox 8glo + glox = 5glox Add '-5glox' to each side of the equation. 8glo + glox + -5glox = 5glox + -5glox Combine like terms: glox + -5glox = -4glox 8glo + -4glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 8glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(2 + -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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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