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Simplifying 13 = 41 + -5ln(2x + 14) Reorder the terms: 13 = 41 + -5ln(14 + 2x) 13 = 41 + (14 * -5ln + 2x * -5ln) 13 = 41 + (-70ln + -10lnx) Solving 13 = 41 + -70ln + -10lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '70ln' to each side of the equation. 13 + 70ln = 41 + -70ln + 70ln + -10lnx Combine like terms: -70ln + 70ln = 0 13 + 70ln = 41 + 0 + -10lnx 13 + 70ln = 41 + -10lnx Add '10lnx' to each side of the equation. 13 + 70ln + 10lnx = 41 + -10lnx + 10lnx Combine like terms: -10lnx + 10lnx = 0 13 + 70ln + 10lnx = 41 + 0 13 + 70ln + 10lnx = 41 Add '-13' to each side of the equation. 13 + 70ln + -13 + 10lnx = 41 + -13 Reorder the terms: 13 + -13 + 70ln + 10lnx = 41 + -13 Combine like terms: 13 + -13 = 0 0 + 70ln + 10lnx = 41 + -13 70ln + 10lnx = 41 + -13 Combine like terms: 41 + -13 = 28 70ln + 10lnx = 28 Reorder the terms: -28 + 70ln + 10lnx = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 70ln + 10lnx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + 35ln + 5lnx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + 35ln + 5lnx)' equal to zero and attempt to solve: Simplifying -14 + 35ln + 5lnx = 0 Solving -14 + 35ln + 5lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 35ln + 14 + 5lnx = 0 + 14 Reorder the terms: -14 + 14 + 35ln + 5lnx = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 35ln + 5lnx = 0 + 14 35ln + 5lnx = 0 + 14 Combine like terms: 0 + 14 = 14 35ln + 5lnx = 14 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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