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Simplifying log(x + 11) + -1log(2) = log(5x + 2) Reorder the terms: glo(11 + x) + -1log(2) = log(5x + 2) (11 * glo + x * glo) + -1log(2) = log(5x + 2) (11glo + glox) + -1log(2) = log(5x + 2) Reorder the terms for easier multiplication: 11glo + glox + -1 * 2glo = log(5x + 2) Multiply -1 * 2 11glo + glox + -2glo = log(5x + 2) Reorder the terms: 11glo + -2glo + glox = log(5x + 2) Combine like terms: 11glo + -2glo = 9glo 9glo + glox = log(5x + 2) Reorder the terms: 9glo + glox = glo(2 + 5x) 9glo + glox = (2 * glo + 5x * glo) 9glo + glox = (2glo + 5glox) Solving 9glo + glox = 2glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glo' to each side of the equation. 9glo + -2glo + glox = 2glo + -2glo + 5glox Combine like terms: 9glo + -2glo = 7glo 7glo + glox = 2glo + -2glo + 5glox Combine like terms: 2glo + -2glo = 0 7glo + glox = 0 + 5glox 7glo + glox = 5glox Add '-5glox' to each side of the equation. 7glo + glox + -5glox = 5glox + -5glox Combine like terms: glox + -5glox = -4glox 7glo + -4glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 7glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(7 + -4x) = 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 '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 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 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Add '4x' to each side of the equation. -4x + 4x = -7 + 4x Combine like terms: -4x + 4x = 0 0 = -7 + 4x Simplifying 0 = -7 + 4x 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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