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Simplifying ln(4x + 4) = ln(2x + -10) Reorder the terms: ln(4 + 4x) = ln(2x + -10) (4 * ln + 4x * ln) = ln(2x + -10) (4ln + 4lnx) = ln(2x + -10) Reorder the terms: 4ln + 4lnx = ln(-10 + 2x) 4ln + 4lnx = (-10 * ln + 2x * ln) 4ln + 4lnx = (-10ln + 2lnx) Solving 4ln + 4lnx = -10ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '10ln' to each side of the equation. 4ln + 10ln + 4lnx = -10ln + 10ln + 2lnx Combine like terms: 4ln + 10ln = 14ln 14ln + 4lnx = -10ln + 10ln + 2lnx Combine like terms: -10ln + 10ln = 0 14ln + 4lnx = 0 + 2lnx 14ln + 4lnx = 2lnx Add '-2lnx' to each side of the equation. 14ln + 4lnx + -2lnx = 2lnx + -2lnx Combine like terms: 4lnx + -2lnx = 2lnx 14ln + 2lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 14ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(7 + x) = 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -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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