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Simplifying (4x + -9) * ln(5) = (x + -4) * ln(5) Reorder the terms: (-9 + 4x) * ln(5) = (x + -4) * ln(5) Reorder the terms for easier multiplication: 5ln(-9 + 4x) = (x + -4) * ln(5) (-9 * 5ln + 4x * 5ln) = (x + -4) * ln(5) (-45ln + 20lnx) = (x + -4) * ln(5) Reorder the terms: -45ln + 20lnx = (-4 + x) * ln(5) Reorder the terms for easier multiplication: -45ln + 20lnx = 5ln(-4 + x) -45ln + 20lnx = (-4 * 5ln + x * 5ln) -45ln + 20lnx = (-20ln + 5lnx) Solving -45ln + 20lnx = -20ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '20ln' to each side of the equation. -45ln + 20ln + 20lnx = -20ln + 20ln + 5lnx Combine like terms: -45ln + 20ln = -25ln -25ln + 20lnx = -20ln + 20ln + 5lnx Combine like terms: -20ln + 20ln = 0 -25ln + 20lnx = 0 + 5lnx -25ln + 20lnx = 5lnx Add '-5lnx' to each side of the equation. -25ln + 20lnx + -5lnx = 5lnx + -5lnx Combine like terms: 20lnx + -5lnx = 15lnx -25ln + 15lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -25ln + 15lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(-5 + 3x) = 0 Ignore the factor 5.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 '(-5 + 3x)' equal to zero and attempt to solve: Simplifying -5 + 3x = 0 Solving -5 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 0 + 5 3x = 0 + 5 Combine like terms: 0 + 5 = 5 3x = 5 Add '-3x' to each side of the equation. 3x + -3x = 5 + -3x Combine like terms: 3x + -3x = 0 0 = 5 + -3x Simplifying 0 = 5 + -3x 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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