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Simplifying ln(7x + 16) + ln(2) = 2ln(x) Reorder the terms: ln(16 + 7x) + ln(2) = 2ln(x) (16 * ln + 7x * ln) + ln(2) = 2ln(x) (16ln + 7lnx) + ln(2) = 2ln(x) Reorder the terms for easier multiplication: 16ln + 7lnx + 2ln = 2ln(x) Reorder the terms: 16ln + 2ln + 7lnx = 2ln(x) Combine like terms: 16ln + 2ln = 18ln 18ln + 7lnx = 2ln(x) Multiply ln * x 18ln + 7lnx = 2lnx Solving 18ln + 7lnx = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. 18ln + 7lnx + -2lnx = 2lnx + -2lnx Combine like terms: 7lnx + -2lnx = 5lnx 18ln + 5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 18ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(18 + 5x) = 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 '(18 + 5x)' equal to zero and attempt to solve: Simplifying 18 + 5x = 0 Solving 18 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + 5x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 5x = 0 + -18 5x = 0 + -18 Combine like terms: 0 + -18 = -18 5x = -18 Add '-5x' to each side of the equation. 5x + -5x = -18 + -5x Combine like terms: 5x + -5x = 0 0 = -18 + -5x Simplifying 0 = -18 + -5x 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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