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Simplifying ln(x + -23) + -1ln(5 + -1x) = ln(4) + ln(x) Reorder the terms: ln(-23 + x) + -1ln(5 + -1x) = ln(4) + ln(x) (-23 * ln + x * ln) + -1ln(5 + -1x) = ln(4) + ln(x) (-23ln + lnx) + -1ln(5 + -1x) = ln(4) + ln(x) -23ln + lnx + (5 * -1ln + -1x * -1ln) = ln(4) + ln(x) -23ln + lnx + (-5ln + 1lnx) = ln(4) + ln(x) Reorder the terms: -23ln + -5ln + lnx + 1lnx = ln(4) + ln(x) Combine like terms: -23ln + -5ln = -28ln -28ln + lnx + 1lnx = ln(4) + ln(x) Combine like terms: lnx + 1lnx = 2lnx -28ln + 2lnx = ln(4) + ln(x) Reorder the terms for easier multiplication: -28ln + 2lnx = 4ln + ln(x) Multiply ln * x -28ln + 2lnx = 4ln + lnx Solving -28ln + 2lnx = 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. -28ln + -4ln + 2lnx = 4ln + -4ln + lnx Combine like terms: -28ln + -4ln = -32ln -32ln + 2lnx = 4ln + -4ln + lnx Combine like terms: 4ln + -4ln = 0 -32ln + 2lnx = 0 + lnx -32ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -32ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -32ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -32ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-32 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying -32 + x = 0 Solving -32 + x = 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 + x = 0 + 32 Combine like terms: -32 + 32 = 0 0 + x = 0 + 32 x = 0 + 32 Combine like terms: 0 + 32 = 32 x = 32 Add '-1x' to each side of the equation. x + -1x = 32 + -1x Combine like terms: x + -1x = 0 0 = 32 + -1x Simplifying 0 = 32 + -1x 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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