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Simplifying 8 + 4ln(5x + 7) = 12 Reorder the terms: 8 + 4ln(7 + 5x) = 12 8 + (7 * 4ln + 5x * 4ln) = 12 8 + (28ln + 20lnx) = 12 Solving 8 + 28ln + 20lnx = 12 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + 28ln + -8 + 20lnx = 12 + -8 Reorder the terms: 8 + -8 + 28ln + 20lnx = 12 + -8 Combine like terms: 8 + -8 = 0 0 + 28ln + 20lnx = 12 + -8 28ln + 20lnx = 12 + -8 Combine like terms: 12 + -8 = 4 28ln + 20lnx = 4 Reorder the terms: -4 + 28ln + 20lnx = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 28ln + 20lnx = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + 7ln + 5lnx) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + 7ln + 5lnx)' equal to zero and attempt to solve: Simplifying -1 + 7ln + 5lnx = 0 Solving -1 + 7ln + 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 + 7ln + 1 + 5lnx = 0 + 1 Reorder the terms: -1 + 1 + 7ln + 5lnx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 7ln + 5lnx = 0 + 1 7ln + 5lnx = 0 + 1 Combine like terms: 0 + 1 = 1 7ln + 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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