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Simplifying ln(x + -4) + ln(6x + -5) = ln * 5 Reorder the terms: ln(-4 + x) + ln(6x + -5) = ln * 5 (-4 * ln + x * ln) + ln(6x + -5) = ln * 5 (-4ln + lnx) + ln(6x + -5) = ln * 5 Reorder the terms: -4ln + lnx + ln(-5 + 6x) = ln * 5 -4ln + lnx + (-5 * ln + 6x * ln) = ln * 5 -4ln + lnx + (-5ln + 6lnx) = ln * 5 Reorder the terms: -4ln + -5ln + lnx + 6lnx = ln * 5 Combine like terms: -4ln + -5ln = -9ln -9ln + lnx + 6lnx = ln * 5 Combine like terms: lnx + 6lnx = 7lnx -9ln + 7lnx = ln * 5 Reorder the terms for easier multiplication: -9ln + 7lnx = 5ln Solving -9ln + 7lnx = 5ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. -9ln + -5ln + 7lnx = 5ln + -5ln Combine like terms: -9ln + -5ln = -14ln -14ln + 7lnx = 5ln + -5ln Combine like terms: 5ln + -5ln = 0 -14ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), '7ln'. 7ln(-2 + x) = 0 Ignore the factor 7.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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