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Simplifying ln(4 + -1x2) + ln(2x + 7) = ln(10x + 25) (4 * ln + -1x2 * ln) + ln(2x + 7) = ln(10x + 25) (4ln + -1lnx2) + ln(2x + 7) = ln(10x + 25) Reorder the terms: 4ln + -1lnx2 + ln(7 + 2x) = ln(10x + 25) 4ln + -1lnx2 + (7 * ln + 2x * ln) = ln(10x + 25) 4ln + -1lnx2 + (7ln + 2lnx) = ln(10x + 25) Reorder the terms: 4ln + 7ln + 2lnx + -1lnx2 = ln(10x + 25) Combine like terms: 4ln + 7ln = 11ln 11ln + 2lnx + -1lnx2 = ln(10x + 25) Reorder the terms: 11ln + 2lnx + -1lnx2 = ln(25 + 10x) 11ln + 2lnx + -1lnx2 = (25 * ln + 10x * ln) 11ln + 2lnx + -1lnx2 = (25ln + 10lnx) Solving 11ln + 2lnx + -1lnx2 = 25ln + 10lnx 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. 11ln + 2lnx + -25ln + -1lnx2 = 25ln + -25ln + 10lnx Reorder the terms: 11ln + -25ln + 2lnx + -1lnx2 = 25ln + -25ln + 10lnx Combine like terms: 11ln + -25ln = -14ln -14ln + 2lnx + -1lnx2 = 25ln + -25ln + 10lnx Combine like terms: 25ln + -25ln = 0 -14ln + 2lnx + -1lnx2 = 0 + 10lnx -14ln + 2lnx + -1lnx2 = 10lnx Add '-10lnx' to each side of the equation. -14ln + 2lnx + -10lnx + -1lnx2 = 10lnx + -10lnx Combine like terms: 2lnx + -10lnx = -8lnx -14ln + -8lnx + -1lnx2 = 10lnx + -10lnx Combine like terms: 10lnx + -10lnx = 0 -14ln + -8lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(14 + 8x + x2) = 0 Ignore the factor -1.Subproblem 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 '(14 + 8x + x2)' equal to zero and attempt to solve: Simplifying 14 + 8x + x2 = 0 Solving 14 + 8x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + 8x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 8x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 8x + x2 = 0 + -14 8x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 8x + x2 = -14 Add '-8x' to each side of the equation. 8x + -8x + x2 = -14 + -8x Combine like terms: 8x + -8x = 0 0 + x2 = -14 + -8x x2 = -14 + -8x Add '-1x2' to each side of the equation. x2 + -1x2 = -14 + -8x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -14 + -8x + -1x2 Simplifying 0 = -14 + -8x + -1x2 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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