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Simplifying ln(3x + -20) = ln(2x + -10) Reorder the terms: ln(-20 + 3x) = ln(2x + -10) (-20 * ln + 3x * ln) = ln(2x + -10) (-20ln + 3lnx) = ln(2x + -10) Reorder the terms: -20ln + 3lnx = ln(-10 + 2x) -20ln + 3lnx = (-10 * ln + 2x * ln) -20ln + 3lnx = (-10ln + 2lnx) Solving -20ln + 3lnx = -10ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '10ln' to each side of the equation. -20ln + 10ln + 3lnx = -10ln + 10ln + 2lnx Combine like terms: -20ln + 10ln = -10ln -10ln + 3lnx = -10ln + 10ln + 2lnx Combine like terms: -10ln + 10ln = 0 -10ln + 3lnx = 0 + 2lnx -10ln + 3lnx = 2lnx Add '-2lnx' to each side of the equation. -10ln + 3lnx + -2lnx = 2lnx + -2lnx Combine like terms: 3lnx + -2lnx = 1lnx -10ln + 1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -10ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 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 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Add '-1x' to each side of the equation. x + -1x = 10 + -1x Combine like terms: x + -1x = 0 0 = 10 + -1x Simplifying 0 = 10 + -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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