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Simplifying ln(x * 2 + 6x + 9) = 4ln(5) Reorder the terms for easier multiplication: ln(2x + 6x + 9) = 4ln(5) Reorder the terms: ln(9 + 2x + 6x) = 4ln(5) Combine like terms: 2x + 6x = 8x ln(9 + 8x) = 4ln(5) (9 * ln + 8x * ln) = 4ln(5) (9ln + 8lnx) = 4ln(5) Reorder the terms for easier multiplication: 9ln + 8lnx = 4 * 5ln Multiply 4 * 5 9ln + 8lnx = 20ln Solving 9ln + 8lnx = 20ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-20ln' to each side of the equation. 9ln + -20ln + 8lnx = 20ln + -20ln Combine like terms: 9ln + -20ln = -11ln -11ln + 8lnx = 20ln + -20ln Combine like terms: 20ln + -20ln = 0 -11ln + 8lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-11 + 8x) = 0Subproblem 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 '(-11 + 8x)' equal to zero and attempt to solve: Simplifying -11 + 8x = 0 Solving -11 + 8x = 0 Move all terms containing l to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 8x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 8x = 0 + 11 8x = 0 + 11 Combine like terms: 0 + 11 = 11 8x = 11 Add '-8x' to each side of the equation. 8x + -8x = 11 + -8x Combine like terms: 8x + -8x = 0 0 = 11 + -8x Simplifying 0 = 11 + -8x 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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