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Simplifying ln(2x) = 2ln(4x + -15) Remove parenthesis around (2x) ln * 2x = 2ln(4x + -15) Reorder the terms for easier multiplication: 2ln * x = 2ln(4x + -15) Multiply ln * x 2lnx = 2ln(4x + -15) Reorder the terms: 2lnx = 2ln(-15 + 4x) 2lnx = (-15 * 2ln + 4x * 2ln) 2lnx = (-30ln + 8lnx) Solving 2lnx = -30ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '30ln' to each side of the equation. 30ln + 2lnx = -30ln + 30ln + 8lnx Combine like terms: -30ln + 30ln = 0 30ln + 2lnx = 0 + 8lnx 30ln + 2lnx = 8lnx Add '-8lnx' to each side of the equation. 30ln + 2lnx + -8lnx = 8lnx + -8lnx Combine like terms: 2lnx + -8lnx = -6lnx 30ln + -6lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 30ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '6ln'. 6ln(5 + -1x) = 0 Ignore the factor 6.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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