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Simplifying ln(5x + 10) = ln(2x + -5) Reorder the terms: ln(10 + 5x) = ln(2x + -5) (10 * ln + 5x * ln) = ln(2x + -5) (10ln + 5lnx) = ln(2x + -5) Reorder the terms: 10ln + 5lnx = ln(-5 + 2x) 10ln + 5lnx = (-5 * ln + 2x * ln) 10ln + 5lnx = (-5ln + 2lnx) Solving 10ln + 5lnx = -5ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. 10ln + 5ln + 5lnx = -5ln + 5ln + 2lnx Combine like terms: 10ln + 5ln = 15ln 15ln + 5lnx = -5ln + 5ln + 2lnx Combine like terms: -5ln + 5ln = 0 15ln + 5lnx = 0 + 2lnx 15ln + 5lnx = 2lnx Add '-2lnx' to each side of the equation. 15ln + 5lnx + -2lnx = 2lnx + -2lnx Combine like terms: 5lnx + -2lnx = 3lnx 15ln + 3lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 15ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(5 + x) = 0 Ignore the factor 3.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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