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Simplifying ln(4x + 1) + ln(4x + -7) + -1ln(9) = 0 Reorder the terms: ln(1 + 4x) + ln(4x + -7) + -1ln(9) = 0 (1 * ln + 4x * ln) + ln(4x + -7) + -1ln(9) = 0 (1ln + 4lnx) + ln(4x + -7) + -1ln(9) = 0 Reorder the terms: 1ln + 4lnx + ln(-7 + 4x) + -1ln(9) = 0 1ln + 4lnx + (-7 * ln + 4x * ln) + -1ln(9) = 0 1ln + 4lnx + (-7ln + 4lnx) + -1ln(9) = 0 Reorder the terms for easier multiplication: 1ln + 4lnx + -7ln + 4lnx + -1 * 9ln = 0 Multiply -1 * 9 1ln + 4lnx + -7ln + 4lnx + -9ln = 0 Reorder the terms: 1ln + -7ln + -9ln + 4lnx + 4lnx = 0 Combine like terms: 1ln + -7ln = -6ln -6ln + -9ln + 4lnx + 4lnx = 0 Combine like terms: -6ln + -9ln = -15ln -15ln + 4lnx + 4lnx = 0 Combine like terms: 4lnx + 4lnx = 8lnx -15ln + 8lnx = 0 Solving -15ln + 8lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(-15 + 8x) = 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 '(-15 + 8x)' equal to zero and attempt to solve: Simplifying -15 + 8x = 0 Solving -15 + 8x = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 8x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 8x = 0 + 15 8x = 0 + 15 Combine like terms: 0 + 15 = 15 8x = 15 Add '-8x' to each side of the equation. 8x + -8x = 15 + -8x Combine like terms: 8x + -8x = 0 0 = 15 + -8x Simplifying 0 = 15 + -8x 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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