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Simplifying 53 = 11 + 6ln(4x + 1) Reorder the terms: 53 = 11 + 6ln(1 + 4x) 53 = 11 + (1 * 6ln + 4x * 6ln) 53 = 11 + (6ln + 24lnx) Solving 53 = 11 + 6ln + 24lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 53 + -6ln = 11 + 6ln + -6ln + 24lnx Combine like terms: 6ln + -6ln = 0 53 + -6ln = 11 + 0 + 24lnx 53 + -6ln = 11 + 24lnx Add '-24lnx' to each side of the equation. 53 + -6ln + -24lnx = 11 + 24lnx + -24lnx Combine like terms: 24lnx + -24lnx = 0 53 + -6ln + -24lnx = 11 + 0 53 + -6ln + -24lnx = 11 Add '-53' to each side of the equation. 53 + -6ln + -53 + -24lnx = 11 + -53 Reorder the terms: 53 + -53 + -6ln + -24lnx = 11 + -53 Combine like terms: 53 + -53 = 0 0 + -6ln + -24lnx = 11 + -53 -6ln + -24lnx = 11 + -53 Combine like terms: 11 + -53 = -42 -6ln + -24lnx = -42 Reorder the terms: 42 + -6ln + -24lnx = -42 + 42 Combine like terms: -42 + 42 = 0 42 + -6ln + -24lnx = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(7 + -1ln + -4lnx) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + -1ln + -4lnx)' equal to zero and attempt to solve: Simplifying 7 + -1ln + -4lnx = 0 Solving 7 + -1ln + -4lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -1ln + -7 + -4lnx = 0 + -7 Reorder the terms: 7 + -7 + -1ln + -4lnx = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1ln + -4lnx = 0 + -7 -1ln + -4lnx = 0 + -7 Combine like terms: 0 + -7 = -7 -1ln + -4lnx = -7 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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