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Simplifying 3ln(5x + 1) + 2 = 5 Reorder the terms: 3ln(1 + 5x) + 2 = 5 (1 * 3ln + 5x * 3ln) + 2 = 5 (3ln + 15lnx) + 2 = 5 Reorder the terms: 2 + 3ln + 15lnx = 5 Solving 2 + 3ln + 15lnx = 5 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 3ln + -2 + 15lnx = 5 + -2 Reorder the terms: 2 + -2 + 3ln + 15lnx = 5 + -2 Combine like terms: 2 + -2 = 0 0 + 3ln + 15lnx = 5 + -2 3ln + 15lnx = 5 + -2 Combine like terms: 5 + -2 = 3 3ln + 15lnx = 3 Reorder the terms: -3 + 3ln + 15lnx = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 3ln + 15lnx = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + ln + 5lnx) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + ln + 5lnx)' equal to zero and attempt to solve: Simplifying -1 + ln + 5lnx = 0 Solving -1 + ln + 5lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + ln + 1 + 5lnx = 0 + 1 Reorder the terms: -1 + 1 + ln + 5lnx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + ln + 5lnx = 0 + 1 ln + 5lnx = 0 + 1 Combine like terms: 0 + 1 = 1 ln + 5lnx = 1 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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