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Simplifying (1 + -8x) * ln(11) = (2x + 3) * ln(9) Reorder the terms for easier multiplication: 11ln(1 + -8x) = (2x + 3) * ln(9) (1 * 11ln + -8x * 11ln) = (2x + 3) * ln(9) (11ln + -88lnx) = (2x + 3) * ln(9) Reorder the terms: 11ln + -88lnx = (3 + 2x) * ln(9) Reorder the terms for easier multiplication: 11ln + -88lnx = 9ln(3 + 2x) 11ln + -88lnx = (3 * 9ln + 2x * 9ln) 11ln + -88lnx = (27ln + 18lnx) Solving 11ln + -88lnx = 27ln + 18lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-27ln' to each side of the equation. 11ln + -27ln + -88lnx = 27ln + -27ln + 18lnx Combine like terms: 11ln + -27ln = -16ln -16ln + -88lnx = 27ln + -27ln + 18lnx Combine like terms: 27ln + -27ln = 0 -16ln + -88lnx = 0 + 18lnx -16ln + -88lnx = 18lnx Add '-18lnx' to each side of the equation. -16ln + -88lnx + -18lnx = 18lnx + -18lnx Combine like terms: -88lnx + -18lnx = -106lnx -16ln + -106lnx = 18lnx + -18lnx Combine like terms: 18lnx + -18lnx = 0 -16ln + -106lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(8 + 53x) = 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 '(8 + 53x)' equal to zero and attempt to solve: Simplifying 8 + 53x = 0 Solving 8 + 53x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 53x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 53x = 0 + -8 53x = 0 + -8 Combine like terms: 0 + -8 = -8 53x = -8 Add '-53x' to each side of the equation. 53x + -53x = -8 + -53x Combine like terms: 53x + -53x = 0 0 = -8 + -53x Simplifying 0 = -8 + -53x 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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