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Simplifying ln(8x + -14) = ln(3x + -36) Reorder the terms: ln(-14 + 8x) = ln(3x + -36) (-14 * ln + 8x * ln) = ln(3x + -36) (-14ln + 8lnx) = ln(3x + -36) Reorder the terms: -14ln + 8lnx = ln(-36 + 3x) -14ln + 8lnx = (-36 * ln + 3x * ln) -14ln + 8lnx = (-36ln + 3lnx) Solving -14ln + 8lnx = -36ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '36ln' to each side of the equation. -14ln + 36ln + 8lnx = -36ln + 36ln + 3lnx Combine like terms: -14ln + 36ln = 22ln 22ln + 8lnx = -36ln + 36ln + 3lnx Combine like terms: -36ln + 36ln = 0 22ln + 8lnx = 0 + 3lnx 22ln + 8lnx = 3lnx Add '-3lnx' to each side of the equation. 22ln + 8lnx + -3lnx = 3lnx + -3lnx Combine like terms: 8lnx + -3lnx = 5lnx 22ln + 5lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 22ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(22 + 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 '(22 + 5x)' equal to zero and attempt to solve: Simplifying 22 + 5x = 0 Solving 22 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + 5x = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 5x = 0 + -22 5x = 0 + -22 Combine like terms: 0 + -22 = -22 5x = -22 Add '-5x' to each side of the equation. 5x + -5x = -22 + -5x Combine like terms: 5x + -5x = 0 0 = -22 + -5x Simplifying 0 = -22 + -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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