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Simplifying 2ln(x + 5) = ln(7x) Reorder the terms: 2ln(5 + x) = ln(7x) (5 * 2ln + x * 2ln) = ln(7x) (10ln + 2lnx) = ln(7x) Remove parenthesis around (7x) 10ln + 2lnx = ln * 7x Reorder the terms for easier multiplication: 10ln + 2lnx = 7ln * x Multiply ln * x 10ln + 2lnx = 7lnx Solving 10ln + 2lnx = 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. 10ln + 2lnx + -7lnx = 7lnx + -7lnx Combine like terms: 2lnx + -7lnx = -5lnx 10ln + -5lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 10ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(2 + -1x) = 0 Ignore the factor 5.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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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