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Simplifying ln(3x + 20) = ln(7x) Reorder the terms: ln(20 + 3x) = ln(7x) (20 * ln + 3x * ln) = ln(7x) (20ln + 3lnx) = ln(7x) Remove parenthesis around (7x) 20ln + 3lnx = ln * 7x Reorder the terms for easier multiplication: 20ln + 3lnx = 7ln * x Multiply ln * x 20ln + 3lnx = 7lnx Solving 20ln + 3lnx = 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. 20ln + 3lnx + -7lnx = 7lnx + -7lnx Combine like terms: 3lnx + -7lnx = -4lnx 20ln + -4lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 20ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(5 + -1x) = 0 Ignore the factor 4.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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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