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Simplifying 3ln(x) + 2ln(4) = ln(128) Multiply ln * x 3lnx + 2ln(4) = ln(128) Reorder the terms for easier multiplication: 3lnx + 2 * 4ln = ln(128) Multiply 2 * 4 3lnx + 8ln = ln(128) Reorder the terms: 8ln + 3lnx = ln(128) Reorder the terms for easier multiplication: 8ln + 3lnx = 128ln Solving 8ln + 3lnx = 128ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-128ln' to each side of the equation. 8ln + -128ln + 3lnx = 128ln + -128ln Combine like terms: 8ln + -128ln = -120ln -120ln + 3lnx = 128ln + -128ln Combine like terms: 128ln + -128ln = 0 -120ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-40 + 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 '(-40 + x)' equal to zero and attempt to solve: Simplifying -40 + x = 0 Solving -40 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 0 + 40 Combine like terms: -40 + 40 = 0 0 + x = 0 + 40 x = 0 + 40 Combine like terms: 0 + 40 = 40 x = 40 Add '-1x' to each side of the equation. x + -1x = 40 + -1x Combine like terms: x + -1x = 0 0 = 40 + -1x Simplifying 0 = 40 + -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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