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Simplifying ln(2x + -5) = ln(25) + -1ln(x + -5) Reorder the terms: ln(-5 + 2x) = ln(25) + -1ln(x + -5) (-5 * ln + 2x * ln) = ln(25) + -1ln(x + -5) (-5ln + 2lnx) = ln(25) + -1ln(x + -5) Reorder the terms for easier multiplication: -5ln + 2lnx = 25ln + -1ln(x + -5) Reorder the terms: -5ln + 2lnx = 25ln + -1ln(-5 + x) -5ln + 2lnx = 25ln + (-5 * -1ln + x * -1ln) -5ln + 2lnx = 25ln + (5ln + -1lnx) Combine like terms: 25ln + 5ln = 30ln -5ln + 2lnx = 30ln + -1lnx Solving -5ln + 2lnx = 30ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-30ln' to each side of the equation. -5ln + -30ln + 2lnx = 30ln + -30ln + -1lnx Combine like terms: -5ln + -30ln = -35ln -35ln + 2lnx = 30ln + -30ln + -1lnx Combine like terms: 30ln + -30ln = 0 -35ln + 2lnx = 0 + -1lnx -35ln + 2lnx = -1lnx Add 'lnx' to each side of the equation. -35ln + 2lnx + lnx = -1lnx + lnx Combine like terms: 2lnx + lnx = 3lnx -35ln + 3lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -35ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-35 + 3x) = 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 '(-35 + 3x)' equal to zero and attempt to solve: Simplifying -35 + 3x = 0 Solving -35 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + 3x = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 3x = 0 + 35 3x = 0 + 35 Combine like terms: 0 + 35 = 35 3x = 35 Add '-3x' to each side of the equation. 3x + -3x = 35 + -3x Combine like terms: 3x + -3x = 0 0 = 35 + -3x Simplifying 0 = 35 + -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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