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Simplifying ln(x + 19) = ln(7x + -8) Reorder the terms: ln(19 + x) = ln(7x + -8) (19 * ln + x * ln) = ln(7x + -8) (19ln + lnx) = ln(7x + -8) Reorder the terms: 19ln + lnx = ln(-8 + 7x) 19ln + lnx = (-8 * ln + 7x * ln) 19ln + lnx = (-8ln + 7lnx) Solving 19ln + lnx = -8ln + 7lnx 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. 19ln + 8ln + lnx = -8ln + 8ln + 7lnx Combine like terms: 19ln + 8ln = 27ln 27ln + lnx = -8ln + 8ln + 7lnx Combine like terms: -8ln + 8ln = 0 27ln + lnx = 0 + 7lnx 27ln + lnx = 7lnx Add '-7lnx' to each side of the equation. 27ln + lnx + -7lnx = 7lnx + -7lnx Combine like terms: lnx + -7lnx = -6lnx 27ln + -6lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 27ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(9 + -2x) = 0 Ignore the factor 3.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 '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Add '2x' to each side of the equation. -2x + 2x = -9 + 2x Combine like terms: -2x + 2x = 0 0 = -9 + 2x Simplifying 0 = -9 + 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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