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