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Simplifying ln(7 + x) + ln(x) = ln(3x + 9) (7 * ln + x * ln) + ln(x) = ln(3x + 9) (7ln + lnx) + ln(x) = ln(3x + 9) Multiply ln * x 7ln + lnx + lnx = ln(3x + 9) Combine like terms: lnx + lnx = 2lnx 7ln + 2lnx = ln(3x + 9) Reorder the terms: 7ln + 2lnx = ln(9 + 3x) 7ln + 2lnx = (9 * ln + 3x * ln) 7ln + 2lnx = (9ln + 3lnx) Solving 7ln + 2lnx = 9ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. 7ln + -9ln + 2lnx = 9ln + -9ln + 3lnx Combine like terms: 7ln + -9ln = -2ln -2ln + 2lnx = 9ln + -9ln + 3lnx Combine like terms: 9ln + -9ln = 0 -2ln + 2lnx = 0 + 3lnx -2ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. -2ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx -2ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -2ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(2 + x) = 0 Ignore the factor -1.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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