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Simplifying ln(9x + 71) = ln(3x + 23) Reorder the terms: ln(71 + 9x) = ln(3x + 23) (71 * ln + 9x * ln) = ln(3x + 23) (71ln + 9lnx) = ln(3x + 23) Reorder the terms: 71ln + 9lnx = ln(23 + 3x) 71ln + 9lnx = (23 * ln + 3x * ln) 71ln + 9lnx = (23ln + 3lnx) Solving 71ln + 9lnx = 23ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-23ln' to each side of the equation. 71ln + -23ln + 9lnx = 23ln + -23ln + 3lnx Combine like terms: 71ln + -23ln = 48ln 48ln + 9lnx = 23ln + -23ln + 3lnx Combine like terms: 23ln + -23ln = 0 48ln + 9lnx = 0 + 3lnx 48ln + 9lnx = 3lnx Add '-3lnx' to each side of the equation. 48ln + 9lnx + -3lnx = 3lnx + -3lnx Combine like terms: 9lnx + -3lnx = 6lnx 48ln + 6lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 48ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '6ln'. 6ln(8 + x) = 0 Ignore the factor 6.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 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 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 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -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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