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Simplifying ln(21) + -1ln(x) = ln(x + -4) Reorder the terms for easier multiplication: 21ln + -1ln(x) = ln(x + -4) Multiply ln * x 21ln + -1lnx = ln(x + -4) Reorder the terms: 21ln + -1lnx = ln(-4 + x) 21ln + -1lnx = (-4 * ln + x * ln) 21ln + -1lnx = (-4ln + lnx) Solving 21ln + -1lnx = -4ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4ln' to each side of the equation. 21ln + 4ln + -1lnx = -4ln + 4ln + lnx Combine like terms: 21ln + 4ln = 25ln 25ln + -1lnx = -4ln + 4ln + lnx Combine like terms: -4ln + 4ln = 0 25ln + -1lnx = 0 + lnx 25ln + -1lnx = lnx Add '-1lnx' to each side of the equation. 25ln + -1lnx + -1lnx = lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx 25ln + -2lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 25ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(25 + -2x) = 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 '(25 + -2x)' equal to zero and attempt to solve: Simplifying 25 + -2x = 0 Solving 25 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -2x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -2x = 0 + -25 -2x = 0 + -25 Combine like terms: 0 + -25 = -25 -2x = -25 Add '2x' to each side of the equation. -2x + 2x = -25 + 2x Combine like terms: -2x + 2x = 0 0 = -25 + 2x Simplifying 0 = -25 + 2x 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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