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Simplifying ln(8x + 5) = ln(3x + -5) Reorder the terms: ln(5 + 8x) = ln(3x + -5) (5 * ln + 8x * ln) = ln(3x + -5) (5ln + 8lnx) = ln(3x + -5) Reorder the terms: 5ln + 8lnx = ln(-5 + 3x) 5ln + 8lnx = (-5 * ln + 3x * ln) 5ln + 8lnx = (-5ln + 3lnx) Solving 5ln + 8lnx = -5ln + 3lnx 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. 5ln + 5ln + 8lnx = -5ln + 5ln + 3lnx Combine like terms: 5ln + 5ln = 10ln 10ln + 8lnx = -5ln + 5ln + 3lnx Combine like terms: -5ln + 5ln = 0 10ln + 8lnx = 0 + 3lnx 10ln + 8lnx = 3lnx Add '-3lnx' to each side of the equation. 10ln + 8lnx + -3lnx = 3lnx + -3lnx Combine like terms: 8lnx + -3lnx = 5lnx 10ln + 5lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 10ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(2 + x) = 0 Ignore the factor 5.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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