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Simplifying ln(7x + 2) = ln(5x + 20) Reorder the terms: ln(2 + 7x) = ln(5x + 20) (2 * ln + 7x * ln) = ln(5x + 20) (2ln + 7lnx) = ln(5x + 20) Reorder the terms: 2ln + 7lnx = ln(20 + 5x) 2ln + 7lnx = (20 * ln + 5x * ln) 2ln + 7lnx = (20ln + 5lnx) Solving 2ln + 7lnx = 20ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-20ln' to each side of the equation. 2ln + -20ln + 7lnx = 20ln + -20ln + 5lnx Combine like terms: 2ln + -20ln = -18ln -18ln + 7lnx = 20ln + -20ln + 5lnx Combine like terms: 20ln + -20ln = 0 -18ln + 7lnx = 0 + 5lnx -18ln + 7lnx = 5lnx Add '-5lnx' to each side of the equation. -18ln + 7lnx + -5lnx = 5lnx + -5lnx Combine like terms: 7lnx + -5lnx = 2lnx -18ln + 2lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -18ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-9 + x) = 0 Ignore the factor 2.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 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 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 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Add '-1x' to each side of the equation. x + -1x = 9 + -1x Combine like terms: x + -1x = 0 0 = 9 + -1x Simplifying 0 = 9 + -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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