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Simplifying 3 + 2logx = log(14x + -3) Reorder the terms: 3 + 2glox = glo(-3 + 14x) 3 + 2glox = (-3 * glo + 14x * glo) 3 + 2glox = (-3glo + 14glox) Solving 3 + 2glox = -3glo + 14glox 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. 3 + 3glo + 2glox = -3glo + 3glo + 14glox Combine like terms: -3glo + 3glo = 0 3 + 3glo + 2glox = 0 + 14glox 3 + 3glo + 2glox = 14glox Add '-14glox' to each side of the equation. 3 + 3glo + 2glox + -14glox = 14glox + -14glox Combine like terms: 2glox + -14glox = -12glox 3 + 3glo + -12glox = 14glox + -14glox Combine like terms: 14glox + -14glox = 0 3 + 3glo + -12glox = 0 Add '-3' to each side of the equation. 3 + 3glo + -3 + -12glox = 0 + -3 Reorder the terms: 3 + -3 + 3glo + -12glox = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3glo + -12glox = 0 + -3 3glo + -12glox = 0 + -3 Combine like terms: 0 + -3 = -3 3glo + -12glox = -3 Reorder the terms: 3 + 3glo + -12glox = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 3glo + -12glox = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + glo + -4glox) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + glo + -4glox)' equal to zero and attempt to solve: Simplifying 1 + glo + -4glox = 0 Solving 1 + glo + -4glox = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + glo + -1 + -4glox = 0 + -1 Reorder the terms: 1 + -1 + glo + -4glox = 0 + -1 Combine like terms: 1 + -1 = 0 0 + glo + -4glox = 0 + -1 glo + -4glox = 0 + -1 Combine like terms: 0 + -1 = -1 glo + -4glox = -1 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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