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