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Simplifying Logx + -1log(x + -3) = log(5x) Reorder the terms: goxL + -1glo(-3 + x) = log(5x) goxL + (-3 * -1glo + x * -1glo) = log(5x) goxL + (3glo + -1glox) = log(5x) Reorder the terms: 3glo + -1glox + goxL = log(5x) Remove parenthesis around (5x) 3glo + -1glox + goxL = glo * 5x Reorder the terms for easier multiplication: 3glo + -1glox + goxL = 5glo * x Multiply glo * x 3glo + -1glox + goxL = 5glox Solving 3glo + -1glox + goxL = 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5glox' to each side of the equation. 3glo + -1glox + -5glox + goxL = 5glox + -5glox Combine like terms: -1glox + -5glox = -6glox 3glo + -6glox + goxL = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 3glo + -6glox + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(3l + -6lx + xL) = 0Subproblem 1
Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(3l + -6lx + xL)' equal to zero and attempt to solve: Simplifying 3l + -6lx + xL = 0 Solving 3l + -6lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-3l' to each side of the equation. 3l + -6lx + -3l + xL = 0 + -3l Reorder the terms: 3l + -3l + -6lx + xL = 0 + -3l Combine like terms: 3l + -3l = 0 0 + -6lx + xL = 0 + -3l -6lx + xL = 0 + -3l Remove the zero: -6lx + xL = -3l Add '6lx' to each side of the equation. -6lx + 6lx + xL = -3l + 6lx Combine like terms: -6lx + 6lx = 0 0 + xL = -3l + 6lx xL = -3l + 6lx Add '-1xL' to each side of the equation. xL + -1xL = -3l + 6lx + -1xL Combine like terms: xL + -1xL = 0 0 = -3l + 6lx + -1xL Simplifying 0 = -3l + 6lx + -1xL 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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