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Simplifying ln(9x + -9) + ln(8x) = 2lnx Reorder the terms: ln(-9 + 9x) + ln(8x) = 2lnx (-9 * ln + 9x * ln) + ln(8x) = 2lnx (-9ln + 9lnx) + ln(8x) = 2lnx Remove parenthesis around (8x) -9ln + 9lnx + ln * 8x = 2lnx Reorder the terms for easier multiplication: -9ln + 9lnx + 8ln * x = 2lnx Multiply ln * x -9ln + 9lnx + 8lnx = 2lnx Combine like terms: 9lnx + 8lnx = 17lnx -9ln + 17lnx = 2lnx Solving -9ln + 17lnx = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. -9ln + 17lnx + -2lnx = 2lnx + -2lnx Combine like terms: 17lnx + -2lnx = 15lnx -9ln + 15lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -9ln + 15lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-3 + 5x) = 0 Ignore the factor 3.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 '(-3 + 5x)' equal to zero and attempt to solve: Simplifying -3 + 5x = 0 Solving -3 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 5x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5x = 0 + 3 5x = 0 + 3 Combine like terms: 0 + 3 = 3 5x = 3 Add '-5x' to each side of the equation. 5x + -5x = 3 + -5x Combine like terms: 5x + -5x = 0 0 = 3 + -5x Simplifying 0 = 3 + -5x 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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