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Simplifying 2ln(x) = ln(x + 4) + ln(2x) Multiply ln * x 2lnx = ln(x + 4) + ln(2x) Reorder the terms: 2lnx = ln(4 + x) + ln(2x) 2lnx = (4 * ln + x * ln) + ln(2x) 2lnx = (4ln + lnx) + ln(2x) Remove parenthesis around (2x) 2lnx = 4ln + lnx + ln * 2x Reorder the terms for easier multiplication: 2lnx = 4ln + lnx + 2ln * x Multiply ln * x 2lnx = 4ln + lnx + 2lnx Combine like terms: lnx + 2lnx = 3lnx 2lnx = 4ln + 3lnx Solving 2lnx = 4ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. -4ln + 2lnx = 4ln + -4ln + 3lnx Combine like terms: 4ln + -4ln = 0 -4ln + 2lnx = 0 + 3lnx -4ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. -4ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx -4ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -4ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(4 + x) = 0 Ignore the factor -1.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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -1x 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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