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Simplifying ln * 4r = ln(7 + -3r) Reorder the terms for easier multiplication: 4ln * r = ln(7 + -3r) Multiply ln * r 4lnr = ln(7 + -3r) 4lnr = (7 * ln + -3r * ln) 4lnr = (7ln + -3lnr) Solving 4lnr = 7ln + -3lnr Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. -7ln + 4lnr = 7ln + -7ln + -3lnr Combine like terms: 7ln + -7ln = 0 -7ln + 4lnr = 0 + -3lnr -7ln + 4lnr = -3lnr Add '3lnr' to each side of the equation. -7ln + 4lnr + 3lnr = -3lnr + 3lnr Combine like terms: 4lnr + 3lnr = 7lnr -7ln + 7lnr = -3lnr + 3lnr Combine like terms: -3lnr + 3lnr = 0 -7ln + 7lnr = 0 Factor out the Greatest Common Factor (GCF), '7ln'. 7ln(-1 + r) = 0 Ignore the factor 7.Subproblem 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 '(-1 + r)' equal to zero and attempt to solve: Simplifying -1 + r = 0 Solving -1 + r = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + r = 0 + 1 r = 0 + 1 Combine like terms: 0 + 1 = 1 r = 1 Add '-1r' to each side of the equation. r + -1r = 1 + -1r Combine like terms: r + -1r = 0 0 = 1 + -1r Simplifying 0 = 1 + -1r 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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