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Simplifying (2x * ln + -5ln) + (x * ln + -5ln) = ln * 25 Multiply x * ln (2lnx + -5ln) + (x * ln + -5ln) = ln * 25 Reorder the terms: (-5ln + 2lnx) + (x * ln + -5ln) = ln * 25 Remove parenthesis around (-5ln + 2lnx) -5ln + 2lnx + (x * ln + -5ln) = ln * 25 Multiply x * ln -5ln + 2lnx + (lnx + -5ln) = ln * 25 Reorder the terms: -5ln + 2lnx + (-5ln + lnx) = ln * 25 Remove parenthesis around (-5ln + lnx) -5ln + 2lnx + -5ln + lnx = ln * 25 Reorder the terms: -5ln + -5ln + 2lnx + lnx = ln * 25 Combine like terms: -5ln + -5ln = -10ln -10ln + 2lnx + lnx = ln * 25 Combine like terms: 2lnx + lnx = 3lnx -10ln + 3lnx = ln * 25 Reorder the terms for easier multiplication: -10ln + 3lnx = 25ln Solving -10ln + 3lnx = 25ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-25ln' to each side of the equation. -10ln + -25ln + 3lnx = 25ln + -25ln Combine like terms: -10ln + -25ln = -35ln -35ln + 3lnx = 25ln + -25ln Combine like terms: 25ln + -25ln = 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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