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Simplifying ln(8) + -1ln(4x + 2) = ln(45) Reorder the terms for easier multiplication: 8ln + -1ln(4x + 2) = ln(45) Reorder the terms: 8ln + -1ln(2 + 4x) = ln(45) 8ln + (2 * -1ln + 4x * -1ln) = ln(45) 8ln + (-2ln + -4lnx) = ln(45) Combine like terms: 8ln + -2ln = 6ln 6ln + -4lnx = ln(45) Reorder the terms for easier multiplication: 6ln + -4lnx = 45ln Solving 6ln + -4lnx = 45ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-45ln' to each side of the equation. 6ln + -45ln + -4lnx = 45ln + -45ln Combine like terms: 6ln + -45ln = -39ln -39ln + -4lnx = 45ln + -45ln Combine like terms: 45ln + -45ln = 0 -39ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(39 + 4x) = 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 '(39 + 4x)' equal to zero and attempt to solve: Simplifying 39 + 4x = 0 Solving 39 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + 4x = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 4x = 0 + -39 4x = 0 + -39 Combine like terms: 0 + -39 = -39 4x = -39 Add '-4x' to each side of the equation. 4x + -4x = -39 + -4x Combine like terms: 4x + -4x = 0 0 = -39 + -4x Simplifying 0 = -39 + -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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