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Simplifying ln(9x + 25) = ln(4x + 5) Reorder the terms: ln(25 + 9x) = ln(4x + 5) (25 * ln + 9x * ln) = ln(4x + 5) (25ln + 9lnx) = ln(4x + 5) Reorder the terms: 25ln + 9lnx = ln(5 + 4x) 25ln + 9lnx = (5 * ln + 4x * ln) 25ln + 9lnx = (5ln + 4lnx) Solving 25ln + 9lnx = 5ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. 25ln + -5ln + 9lnx = 5ln + -5ln + 4lnx Combine like terms: 25ln + -5ln = 20ln 20ln + 9lnx = 5ln + -5ln + 4lnx Combine like terms: 5ln + -5ln = 0 20ln + 9lnx = 0 + 4lnx 20ln + 9lnx = 4lnx Add '-4lnx' to each side of the equation. 20ln + 9lnx + -4lnx = 4lnx + -4lnx Combine like terms: 9lnx + -4lnx = 5lnx 20ln + 5lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 20ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(4 + x) = 0 Ignore the factor 5.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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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