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Simplifying 2ln(x) + ln(6x + 7) = ln(9x + -2) Multiply ln * x 2lnx + ln(6x + 7) = ln(9x + -2) Reorder the terms: 2lnx + ln(7 + 6x) = ln(9x + -2) 2lnx + (7 * ln + 6x * ln) = ln(9x + -2) 2lnx + (7ln + 6lnx) = ln(9x + -2) Reorder the terms: 7ln + 2lnx + 6lnx = ln(9x + -2) Combine like terms: 2lnx + 6lnx = 8lnx 7ln + 8lnx = ln(9x + -2) Reorder the terms: 7ln + 8lnx = ln(-2 + 9x) 7ln + 8lnx = (-2 * ln + 9x * ln) 7ln + 8lnx = (-2ln + 9lnx) Solving 7ln + 8lnx = -2ln + 9lnx 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. 7ln + 2ln + 8lnx = -2ln + 2ln + 9lnx Combine like terms: 7ln + 2ln = 9ln 9ln + 8lnx = -2ln + 2ln + 9lnx Combine like terms: -2ln + 2ln = 0 9ln + 8lnx = 0 + 9lnx 9ln + 8lnx = 9lnx Add '-9lnx' to each side of the equation. 9ln + 8lnx + -9lnx = 9lnx + -9lnx Combine like terms: 8lnx + -9lnx = -1lnx 9ln + -1lnx = 9lnx + -9lnx Combine like terms: 9lnx + -9lnx = 0 9ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + -1x) = 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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 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 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Add 'x' to each side of the equation. -1x + x = -9 + x Combine like terms: -1x + x = 0 0 = -9 + x Simplifying 0 = -9 + x 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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