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Simplifying ln(4x + -3) + ln(x + 3) = ln(4x2 + 10) Reorder the terms: ln(-3 + 4x) + ln(x + 3) = ln(4x2 + 10) (-3 * ln + 4x * ln) + ln(x + 3) = ln(4x2 + 10) (-3ln + 4lnx) + ln(x + 3) = ln(4x2 + 10) Reorder the terms: -3ln + 4lnx + ln(3 + x) = ln(4x2 + 10) -3ln + 4lnx + (3 * ln + x * ln) = ln(4x2 + 10) -3ln + 4lnx + (3ln + lnx) = ln(4x2 + 10) Reorder the terms: -3ln + 3ln + 4lnx + lnx = ln(4x2 + 10) Combine like terms: -3ln + 3ln = 0 0 + 4lnx + lnx = ln(4x2 + 10) 4lnx + lnx = ln(4x2 + 10) Combine like terms: 4lnx + lnx = 5lnx 5lnx = ln(4x2 + 10) Reorder the terms: 5lnx = ln(10 + 4x2) 5lnx = (10 * ln + 4x2 * ln) 5lnx = (10ln + 4lnx2) Solving 5lnx = 10ln + 4lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. -10ln + 5lnx = 10ln + -10ln + 4lnx2 Combine like terms: 10ln + -10ln = 0 -10ln + 5lnx = 0 + 4lnx2 -10ln + 5lnx = 4lnx2 Add '-4lnx2' to each side of the equation. -10ln + 5lnx + -4lnx2 = 4lnx2 + -4lnx2 Combine like terms: 4lnx2 + -4lnx2 = 0 -10ln + 5lnx + -4lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + 5x + -4x2) = 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 '(-10 + 5x + -4x2)' equal to zero and attempt to solve: Simplifying -10 + 5x + -4x2 = 0 Solving -10 + 5x + -4x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 5x + 10 + -4x2 = 0 + 10 Reorder the terms: -10 + 10 + 5x + -4x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 5x + -4x2 = 0 + 10 5x + -4x2 = 0 + 10 Combine like terms: 0 + 10 = 10 5x + -4x2 = 10 Add '-5x' to each side of the equation. 5x + -5x + -4x2 = 10 + -5x Combine like terms: 5x + -5x = 0 0 + -4x2 = 10 + -5x -4x2 = 10 + -5x Add '4x2' to each side of the equation. -4x2 + 4x2 = 10 + -5x + 4x2 Combine like terms: -4x2 + 4x2 = 0 0 = 10 + -5x + 4x2 Simplifying 0 = 10 + -5x + 4x2 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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