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Simplifying ln(10x + 17) = ln(x + 1) + ln(2x + -1) Reorder the terms: ln(17 + 10x) = ln(x + 1) + ln(2x + -1) (17 * ln + 10x * ln) = ln(x + 1) + ln(2x + -1) (17ln + 10lnx) = ln(x + 1) + ln(2x + -1) Reorder the terms: 17ln + 10lnx = ln(1 + x) + ln(2x + -1) 17ln + 10lnx = (1 * ln + x * ln) + ln(2x + -1) 17ln + 10lnx = (1ln + lnx) + ln(2x + -1) Reorder the terms: 17ln + 10lnx = 1ln + lnx + ln(-1 + 2x) 17ln + 10lnx = 1ln + lnx + (-1 * ln + 2x * ln) 17ln + 10lnx = 1ln + lnx + (-1ln + 2lnx) Reorder the terms: 17ln + 10lnx = 1ln + -1ln + lnx + 2lnx Combine like terms: 1ln + -1ln = 0 17ln + 10lnx = 0 + lnx + 2lnx 17ln + 10lnx = lnx + 2lnx Combine like terms: lnx + 2lnx = 3lnx 17ln + 10lnx = 3lnx Solving 17ln + 10lnx = 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3lnx' to each side of the equation. 17ln + 10lnx + -3lnx = 3lnx + -3lnx Combine like terms: 10lnx + -3lnx = 7lnx 17ln + 7lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 17ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(17 + 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 '(17 + 7x)' equal to zero and attempt to solve: Simplifying 17 + 7x = 0 Solving 17 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 7x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 7x = 0 + -17 7x = 0 + -17 Combine like terms: 0 + -17 = -17 7x = -17 Add '-7x' to each side of the equation. 7x + -7x = -17 + -7x Combine like terms: 7x + -7x = 0 0 = -17 + -7x Simplifying 0 = -17 + -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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