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Simplifying ln(8x + 5) = ln(6x + -18) Reorder the terms: ln(5 + 8x) = ln(6x + -18) (5 * ln + 8x * ln) = ln(6x + -18) (5ln + 8lnx) = ln(6x + -18) Reorder the terms: 5ln + 8lnx = ln(-18 + 6x) 5ln + 8lnx = (-18 * ln + 6x * ln) 5ln + 8lnx = (-18ln + 6lnx) Solving 5ln + 8lnx = -18ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '18ln' to each side of the equation. 5ln + 18ln + 8lnx = -18ln + 18ln + 6lnx Combine like terms: 5ln + 18ln = 23ln 23ln + 8lnx = -18ln + 18ln + 6lnx Combine like terms: -18ln + 18ln = 0 23ln + 8lnx = 0 + 6lnx 23ln + 8lnx = 6lnx Add '-6lnx' to each side of the equation. 23ln + 8lnx + -6lnx = 6lnx + -6lnx Combine like terms: 8lnx + -6lnx = 2lnx 23ln + 2lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 23ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(23 + 2x) = 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 '(23 + 2x)' equal to zero and attempt to solve: Simplifying 23 + 2x = 0 Solving 23 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + 2x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 2x = 0 + -23 2x = 0 + -23 Combine like terms: 0 + -23 = -23 2x = -23 Add '-2x' to each side of the equation. 2x + -2x = -23 + -2x Combine like terms: 2x + -2x = 0 0 = -23 + -2x Simplifying 0 = -23 + -2x 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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