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Simplifying ln(20) = ln(x + 1) + -1ln(13) Reorder the terms for easier multiplication: 20ln = ln(x + 1) + -1ln(13) Reorder the terms: 20ln = ln(1 + x) + -1ln(13) 20ln = (1 * ln + x * ln) + -1ln(13) 20ln = (1ln + lnx) + -1ln(13) Reorder the terms for easier multiplication: 20ln = 1ln + lnx + -1 * 13ln Multiply -1 * 13 20ln = 1ln + lnx + -13ln Reorder the terms: 20ln = 1ln + -13ln + lnx Combine like terms: 1ln + -13ln = -12ln 20ln = -12ln + lnx Solving 20ln = -12ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '12ln' to each side of the equation. 20ln + 12ln = -12ln + 12ln + lnx Combine like terms: 20ln + 12ln = 32ln 32ln = -12ln + 12ln + lnx Combine like terms: -12ln + 12ln = 0 32ln = 0 + lnx 32ln = lnx Add '-1lnx' to each side of the equation. 32ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 32ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(32 + -1x) = 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 '(32 + -1x)' equal to zero and attempt to solve: Simplifying 32 + -1x = 0 Solving 32 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + -1x = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -1x = 0 + -32 -1x = 0 + -32 Combine like terms: 0 + -32 = -32 -1x = -32 Add 'x' to each side of the equation. -1x + x = -32 + x Combine like terms: -1x + x = 0 0 = -32 + x Simplifying 0 = -32 + x 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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