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Simplifying ln(9x + 8) + -1ln(x) = ln(10) Reorder the terms: ln(8 + 9x) + -1ln(x) = ln(10) (8 * ln + 9x * ln) + -1ln(x) = ln(10) (8ln + 9lnx) + -1ln(x) = ln(10) Multiply ln * x 8ln + 9lnx + -1lnx = ln(10) Combine like terms: 9lnx + -1lnx = 8lnx 8ln + 8lnx = ln(10) Reorder the terms for easier multiplication: 8ln + 8lnx = 10ln Solving 8ln + 8lnx = 10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. 8ln + -10ln + 8lnx = 10ln + -10ln Combine like terms: 8ln + -10ln = -2ln -2ln + 8lnx = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -2ln + 8lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-1 + 4x) = 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 '(-1 + 4x)' equal to zero and attempt to solve: Simplifying -1 + 4x = 0 Solving -1 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4x = 0 + 1 4x = 0 + 1 Combine like terms: 0 + 1 = 1 4x = 1 Add '-4x' to each side of the equation. 4x + -4x = 1 + -4x Combine like terms: 4x + -4x = 0 0 = 1 + -4x Simplifying 0 = 1 + -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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