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Simplifying ln(x + 3) = ln(8x + -5) Reorder the terms: ln(3 + x) = ln(8x + -5) (3 * ln + x * ln) = ln(8x + -5) (3ln + lnx) = ln(8x + -5) Reorder the terms: 3ln + lnx = ln(-5 + 8x) 3ln + lnx = (-5 * ln + 8x * ln) 3ln + lnx = (-5ln + 8lnx) Solving 3ln + lnx = -5ln + 8lnx 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. 3ln + 5ln + lnx = -5ln + 5ln + 8lnx Combine like terms: 3ln + 5ln = 8ln 8ln + lnx = -5ln + 5ln + 8lnx Combine like terms: -5ln + 5ln = 0 8ln + lnx = 0 + 8lnx 8ln + lnx = 8lnx Add '-8lnx' to each side of the equation. 8ln + lnx + -8lnx = 8lnx + -8lnx Combine like terms: lnx + -8lnx = -7lnx 8ln + -7lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 8ln + -7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(8 + -7x) = 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 '(8 + -7x)' equal to zero and attempt to solve: Simplifying 8 + -7x = 0 Solving 8 + -7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7x = 0 + -8 -7x = 0 + -8 Combine like terms: 0 + -8 = -8 -7x = -8 Add '7x' to each side of the equation. -7x + 7x = -8 + 7x Combine like terms: -7x + 7x = 0 0 = -8 + 7x Simplifying 0 = -8 + 7x 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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