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Simplifying ln(9x + 14) + -1lnx = 10ln Reorder the terms: ln(14 + 9x) + -1lnx = 10ln (14 * ln + 9x * ln) + -1lnx = 10ln (14ln + 9lnx) + -1lnx = 10ln Combine like terms: 9lnx + -1lnx = 8lnx 14ln + 8lnx = 10ln Solving 14ln + 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. 14ln + -10ln + 8lnx = 10ln + -10ln Combine like terms: 14ln + -10ln = 4ln 4ln + 8lnx = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 4ln + 8lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(1 + 2x) = 0 Ignore the factor 4.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 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -2x 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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