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Simplifying 3ln(2) + ln(8) = 2ln(4x) Reorder the terms for easier multiplication: 3 * 2ln + ln(8) = 2ln(4x) Multiply 3 * 2 6ln + ln(8) = 2ln(4x) Reorder the terms for easier multiplication: 6ln + 8ln = 2ln(4x) Combine like terms: 6ln + 8ln = 14ln 14ln = 2ln(4x) Remove parenthesis around (4x) 14ln = 2ln * 4x Reorder the terms for easier multiplication: 14ln = 2 * 4ln * x Multiply 2 * 4 14ln = 8ln * x Multiply ln * x 14ln = 8lnx Solving 14ln = 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8lnx' to each side of the equation. 14ln + -8lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 14ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(7 + -4x) = 0 Ignore the factor 2.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 '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Add '4x' to each side of the equation. -4x + 4x = -7 + 4x Combine like terms: -4x + 4x = 0 0 = -7 + 4x Simplifying 0 = -7 + 4x 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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