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Simplifying Log13(-2x + 1) = Log13(-3x + -1) Reorder the terms: g13oL(1 + -2x) = Log13(-3x + -1) (1 * g13oL + -2x * g13oL) = Log13(-3x + -1) (1g13oL + -2g13oxL) = Log13(-3x + -1) Reorder the terms: 1g13oL + -2g13oxL = g13oL(-1 + -3x) 1g13oL + -2g13oxL = (-1 * g13oL + -3x * g13oL) 1g13oL + -2g13oxL = (-1g13oL + -3g13oxL) Solving 1g13oL + -2g13oxL = -1g13oL + -3g13oxL Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add 'g13oL' to each side of the equation. 1g13oL + g13oL + -2g13oxL = -1g13oL + g13oL + -3g13oxL Combine like terms: 1g13oL + g13oL = 2g13oL 2g13oL + -2g13oxL = -1g13oL + g13oL + -3g13oxL Combine like terms: -1g13oL + g13oL = 0 2g13oL + -2g13oxL = 0 + -3g13oxL 2g13oL + -2g13oxL = -3g13oxL Add '3g13oxL' to each side of the equation. 2g13oL + -2g13oxL + 3g13oxL = -3g13oxL + 3g13oxL Combine like terms: -2g13oxL + 3g13oxL = 1g13oxL 2g13oL + 1g13oxL = -3g13oxL + 3g13oxL Combine like terms: -3g13oxL + 3g13oxL = 0 2g13oL + 1g13oxL = 0 Factor out the Greatest Common Factor (GCF), 'g13oL'. g13oL(2 + x) = 0Subproblem 1
Set the factor 'g13oL' equal to zero and attempt to solve: Simplifying g13oL = 0 Solving g13oL = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g13oL = 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 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -1x 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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