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Simplifying ln(9x + 80) = ln(8x + 71) Reorder the terms: ln(80 + 9x) = ln(8x + 71) (80 * ln + 9x * ln) = ln(8x + 71) (80ln + 9lnx) = ln(8x + 71) Reorder the terms: 80ln + 9lnx = ln(71 + 8x) 80ln + 9lnx = (71 * ln + 8x * ln) 80ln + 9lnx = (71ln + 8lnx) Solving 80ln + 9lnx = 71ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-71ln' to each side of the equation. 80ln + -71ln + 9lnx = 71ln + -71ln + 8lnx Combine like terms: 80ln + -71ln = 9ln 9ln + 9lnx = 71ln + -71ln + 8lnx Combine like terms: 71ln + -71ln = 0 9ln + 9lnx = 0 + 8lnx 9ln + 9lnx = 8lnx Add '-8lnx' to each side of the equation. 9ln + 9lnx + -8lnx = 8lnx + -8lnx Combine like terms: 9lnx + -8lnx = 1lnx 9ln + 1lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 9ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + x) = 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 '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Add '-1x' to each side of the equation. x + -1x = -9 + -1x Combine like terms: x + -1x = 0 0 = -9 + -1x Simplifying 0 = -9 + -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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