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Simplifying ln(2x + -5) + ln(x) = ln(3) + ln(-2x + 5) Reorder the terms: ln(-5 + 2x) + ln(x) = ln(3) + ln(-2x + 5) (-5 * ln + 2x * ln) + ln(x) = ln(3) + ln(-2x + 5) (-5ln + 2lnx) + ln(x) = ln(3) + ln(-2x + 5) Multiply ln * x -5ln + 2lnx + lnx = ln(3) + ln(-2x + 5) Combine like terms: 2lnx + lnx = 3lnx -5ln + 3lnx = ln(3) + ln(-2x + 5) Reorder the terms for easier multiplication: -5ln + 3lnx = 3ln + ln(-2x + 5) Reorder the terms: -5ln + 3lnx = 3ln + ln(5 + -2x) -5ln + 3lnx = 3ln + (5 * ln + -2x * ln) -5ln + 3lnx = 3ln + (5ln + -2lnx) Combine like terms: 3ln + 5ln = 8ln -5ln + 3lnx = 8ln + -2lnx Solving -5ln + 3lnx = 8ln + -2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. -5ln + -8ln + 3lnx = 8ln + -8ln + -2lnx Combine like terms: -5ln + -8ln = -13ln -13ln + 3lnx = 8ln + -8ln + -2lnx Combine like terms: 8ln + -8ln = 0 -13ln + 3lnx = 0 + -2lnx -13ln + 3lnx = -2lnx Add '2lnx' to each side of the equation. -13ln + 3lnx + 2lnx = -2lnx + 2lnx Combine like terms: 3lnx + 2lnx = 5lnx -13ln + 5lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -13ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + 5x) = 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 '(-13 + 5x)' equal to zero and attempt to solve: Simplifying -13 + 5x = 0 Solving -13 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 5x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 5x = 0 + 13 5x = 0 + 13 Combine like terms: 0 + 13 = 13 5x = 13 Add '-5x' to each side of the equation. 5x + -5x = 13 + -5x Combine like terms: 5x + -5x = 0 0 = 13 + -5x Simplifying 0 = 13 + -5x 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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