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Simplifying 4ln(x + 9) = 7ln(x) Reorder the terms: 4ln(9 + x) = 7ln(x) (9 * 4ln + x * 4ln) = 7ln(x) (36ln + 4lnx) = 7ln(x) Multiply ln * x 36ln + 4lnx = 7lnx Solving 36ln + 4lnx = 7lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7lnx' to each side of the equation. 36ln + 4lnx + -7lnx = 7lnx + -7lnx Combine like terms: 4lnx + -7lnx = -3lnx 36ln + -3lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 36ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(12 + -1x) = 0 Ignore the factor 3.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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Add 'x' to each side of the equation. -1x + x = -12 + x Combine like terms: -1x + x = 0 0 = -12 + x Simplifying 0 = -12 + x 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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