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Simplifying 7ln(x + 5) = 4lnx Reorder the terms: 7ln(5 + x) = 4lnx (5 * 7ln + x * 7ln) = 4lnx (35ln + 7lnx) = 4lnx Solving 35ln + 7lnx = 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4lnx' to each side of the equation. 35ln + 7lnx + -4lnx = 4lnx + -4lnx Combine like terms: 7lnx + -4lnx = 3lnx 35ln + 3lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 35ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(35 + 3x) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(35 + 3x)' equal to zero and attempt to solve: Simplifying 35 + 3x = 0 Solving 35 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + 3x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 3x = 0 + -35 3x = 0 + -35 Combine like terms: 0 + -35 = -35 3x = -35 Add '-3x' to each side of the equation. 3x + -3x = -35 + -3x Combine like terms: 3x + -3x = 0 0 = -35 + -3x Simplifying 0 = -35 + -3x 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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