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Simplifying 6ln(5x + 3) + 7 = 49 Reorder the terms: 6ln(3 + 5x) + 7 = 49 (3 * 6ln + 5x * 6ln) + 7 = 49 (18ln + 30lnx) + 7 = 49 Reorder the terms: 7 + 18ln + 30lnx = 49 Solving 7 + 18ln + 30lnx = 49 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + 18ln + -7 + 30lnx = 49 + -7 Reorder the terms: 7 + -7 + 18ln + 30lnx = 49 + -7 Combine like terms: 7 + -7 = 0 0 + 18ln + 30lnx = 49 + -7 18ln + 30lnx = 49 + -7 Combine like terms: 49 + -7 = 42 18ln + 30lnx = 42 Reorder the terms: -42 + 18ln + 30lnx = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 18ln + 30lnx = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-7 + 3ln + 5lnx) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-7 + 3ln + 5lnx)' equal to zero and attempt to solve: Simplifying -7 + 3ln + 5lnx = 0 Solving -7 + 3ln + 5lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 3ln + 7 + 5lnx = 0 + 7 Reorder the terms: -7 + 7 + 3ln + 5lnx = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3ln + 5lnx = 0 + 7 3ln + 5lnx = 0 + 7 Combine like terms: 0 + 7 = 7 3ln + 5lnx = 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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