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Simplifying ln(5x + -6) + ln(x + -1) = ln(6) Reorder the terms: ln(-6 + 5x) + ln(x + -1) = ln(6) (-6 * ln + 5x * ln) + ln(x + -1) = ln(6) (-6ln + 5lnx) + ln(x + -1) = ln(6) Reorder the terms: -6ln + 5lnx + ln(-1 + x) = ln(6) -6ln + 5lnx + (-1 * ln + x * ln) = ln(6) -6ln + 5lnx + (-1ln + lnx) = ln(6) Reorder the terms: -6ln + -1ln + 5lnx + lnx = ln(6) Combine like terms: -6ln + -1ln = -7ln -7ln + 5lnx + lnx = ln(6) Combine like terms: 5lnx + lnx = 6lnx -7ln + 6lnx = ln(6) Reorder the terms for easier multiplication: -7ln + 6lnx = 6ln Solving -7ln + 6lnx = 6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. -7ln + -6ln + 6lnx = 6ln + -6ln Combine like terms: -7ln + -6ln = -13ln -13ln + 6lnx = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 -13ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + 6x) = 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 '(-13 + 6x)' equal to zero and attempt to solve: Simplifying -13 + 6x = 0 Solving -13 + 6x = 0 Move all terms containing l to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 6x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 6x = 0 + 13 6x = 0 + 13 Combine like terms: 0 + 13 = 13 6x = 13 Add '-6x' to each side of the equation. 6x + -6x = 13 + -6x Combine like terms: 6x + -6x = 0 0 = 13 + -6x Simplifying 0 = 13 + -6x 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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