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Simplifying 2lnx = ln(17x) + ln(2 + -1x) Remove parenthesis around (17x) 2lnx = ln * 17x + ln(2 + -1x) Reorder the terms for easier multiplication: 2lnx = 17ln * x + ln(2 + -1x) Multiply ln * x 2lnx = 17lnx + ln(2 + -1x) 2lnx = 17lnx + (2 * ln + -1x * ln) 2lnx = 17lnx + (2ln + -1lnx) Reorder the terms: 2lnx = 2ln + 17lnx + -1lnx Combine like terms: 17lnx + -1lnx = 16lnx 2lnx = 2ln + 16lnx Solving 2lnx = 2ln + 16lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. -2ln + 2lnx = 2ln + -2ln + 16lnx Combine like terms: 2ln + -2ln = 0 -2ln + 2lnx = 0 + 16lnx -2ln + 2lnx = 16lnx Add '-16lnx' to each side of the equation. -2ln + 2lnx + -16lnx = 16lnx + -16lnx Combine like terms: 2lnx + -16lnx = -14lnx -2ln + -14lnx = 16lnx + -16lnx Combine like terms: 16lnx + -16lnx = 0 -2ln + -14lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(1 + 7x) = 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 '(1 + 7x)' equal to zero and attempt to solve: Simplifying 1 + 7x = 0 Solving 1 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7x = 0 + -1 7x = 0 + -1 Combine like terms: 0 + -1 = -1 7x = -1 Add '-7x' to each side of the equation. 7x + -7x = -1 + -7x Combine like terms: 7x + -7x = 0 0 = -1 + -7x Simplifying 0 = -1 + -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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