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Simplifying ln(5x + -6) + ln(x + -6) = ln(36) Reorder the terms: ln(-6 + 5x) + ln(x + -6) = ln(36) (-6 * ln + 5x * ln) + ln(x + -6) = ln(36) (-6ln + 5lnx) + ln(x + -6) = ln(36) Reorder the terms: -6ln + 5lnx + ln(-6 + x) = ln(36) -6ln + 5lnx + (-6 * ln + x * ln) = ln(36) -6ln + 5lnx + (-6ln + lnx) = ln(36) Reorder the terms: -6ln + -6ln + 5lnx + lnx = ln(36) Combine like terms: -6ln + -6ln = -12ln -12ln + 5lnx + lnx = ln(36) Combine like terms: 5lnx + lnx = 6lnx -12ln + 6lnx = ln(36) Reorder the terms for easier multiplication: -12ln + 6lnx = 36ln Solving -12ln + 6lnx = 36ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-36ln' to each side of the equation. -12ln + -36ln + 6lnx = 36ln + -36ln Combine like terms: -12ln + -36ln = -48ln -48ln + 6lnx = 36ln + -36ln Combine like terms: 36ln + -36ln = 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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