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Simplifying ln(x + -2) + ln(x) = ln(5x + -12) Reorder the terms: ln(-2 + x) + ln(x) = ln(5x + -12) (-2 * ln + x * ln) + ln(x) = ln(5x + -12) (-2ln + lnx) + ln(x) = ln(5x + -12) Multiply ln * x -2ln + lnx + lnx = ln(5x + -12) Combine like terms: lnx + lnx = 2lnx -2ln + 2lnx = ln(5x + -12) Reorder the terms: -2ln + 2lnx = ln(-12 + 5x) -2ln + 2lnx = (-12 * ln + 5x * ln) -2ln + 2lnx = (-12ln + 5lnx) Solving -2ln + 2lnx = -12ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '12ln' to each side of the equation. -2ln + 12ln + 2lnx = -12ln + 12ln + 5lnx Combine like terms: -2ln + 12ln = 10ln 10ln + 2lnx = -12ln + 12ln + 5lnx Combine like terms: -12ln + 12ln = 0 10ln + 2lnx = 0 + 5lnx 10ln + 2lnx = 5lnx Add '-5lnx' to each side of the equation. 10ln + 2lnx + -5lnx = 5lnx + -5lnx Combine like terms: 2lnx + -5lnx = -3lnx 10ln + -3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 10ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(10 + -3x) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 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 '(10 + -3x)' equal to zero and attempt to solve: Simplifying 10 + -3x = 0 Solving 10 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3x = 0 + -10 -3x = 0 + -10 Combine like terms: 0 + -10 = -10 -3x = -10 Add '3x' to each side of the equation. -3x + 3x = -10 + 3x Combine like terms: -3x + 3x = 0 0 = -10 + 3x Simplifying 0 = -10 + 3x 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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