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Simplifying 60 = 10 + 5ln(4x + 3) Reorder the terms: 60 = 10 + 5ln(3 + 4x) 60 = 10 + (3 * 5ln + 4x * 5ln) 60 = 10 + (15ln + 20lnx) Solving 60 = 10 + 15ln + 20lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. 60 + -15ln = 10 + 15ln + -15ln + 20lnx Combine like terms: 15ln + -15ln = 0 60 + -15ln = 10 + 0 + 20lnx 60 + -15ln = 10 + 20lnx Add '-20lnx' to each side of the equation. 60 + -15ln + -20lnx = 10 + 20lnx + -20lnx Combine like terms: 20lnx + -20lnx = 0 60 + -15ln + -20lnx = 10 + 0 60 + -15ln + -20lnx = 10 Add '-60' to each side of the equation. 60 + -15ln + -60 + -20lnx = 10 + -60 Reorder the terms: 60 + -60 + -15ln + -20lnx = 10 + -60 Combine like terms: 60 + -60 = 0 0 + -15ln + -20lnx = 10 + -60 -15ln + -20lnx = 10 + -60 Combine like terms: 10 + -60 = -50 -15ln + -20lnx = -50 Reorder the terms: 50 + -15ln + -20lnx = -50 + 50 Combine like terms: -50 + 50 = 0 50 + -15ln + -20lnx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(10 + -3ln + -4lnx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + -3ln + -4lnx)' equal to zero and attempt to solve: Simplifying 10 + -3ln + -4lnx = 0 Solving 10 + -3ln + -4lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -3ln + -10 + -4lnx = 0 + -10 Reorder the terms: 10 + -10 + -3ln + -4lnx = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3ln + -4lnx = 0 + -10 -3ln + -4lnx = 0 + -10 Combine like terms: 0 + -10 = -10 -3ln + -4lnx = -10 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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