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Simplifying 2ln(2x) + -6ln(2) = ln(x + -3) Remove parenthesis around (2x) 2ln * 2x + -6ln(2) = ln(x + -3) Reorder the terms for easier multiplication: 2 * 2ln * x + -6ln(2) = ln(x + -3) Multiply 2 * 2 4ln * x + -6ln(2) = ln(x + -3) Multiply ln * x 4lnx + -6ln(2) = ln(x + -3) Reorder the terms for easier multiplication: 4lnx + -6 * 2ln = ln(x + -3) Multiply -6 * 2 4lnx + -12ln = ln(x + -3) Reorder the terms: -12ln + 4lnx = ln(x + -3) Reorder the terms: -12ln + 4lnx = ln(-3 + x) -12ln + 4lnx = (-3 * ln + x * ln) -12ln + 4lnx = (-3ln + lnx) Solving -12ln + 4lnx = -3ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '3ln' to each side of the equation. -12ln + 3ln + 4lnx = -3ln + 3ln + lnx Combine like terms: -12ln + 3ln = -9ln -9ln + 4lnx = -3ln + 3ln + lnx Combine like terms: -3ln + 3ln = 0 -9ln + 4lnx = 0 + lnx -9ln + 4lnx = lnx Add '-1lnx' to each side of the equation. -9ln + 4lnx + -1lnx = lnx + -1lnx Combine like terms: 4lnx + -1lnx = 3lnx -9ln + 3lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -9ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-3 + x) = 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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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