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Simplifying ln(x + 2) * ln(4) = ln(7) + -1ln(x) Reorder the terms: ln(2 + x) * ln(4) = ln(7) + -1ln(x) Reorder the terms for easier multiplication: 4ln * ln(2 + x) = ln(7) + -1ln(x) Multiply ln * ln 4l2n2(2 + x) = ln(7) + -1ln(x) (2 * 4l2n2 + x * 4l2n2) = ln(7) + -1ln(x) (8l2n2 + 4l2n2x) = ln(7) + -1ln(x) Reorder the terms for easier multiplication: 8l2n2 + 4l2n2x = 7ln + -1ln(x) Multiply ln * x 8l2n2 + 4l2n2x = 7ln + -1lnx Solving 8l2n2 + 4l2n2x = 7ln + -1lnx Solving for variable 'l'. Reorder the terms: -7ln + lnx + 8l2n2 + 4l2n2x = 7ln + -1lnx + -7ln + lnx Reorder the terms: -7ln + lnx + 8l2n2 + 4l2n2x = 7ln + -7ln + -1lnx + lnx Combine like terms: 7ln + -7ln = 0 -7ln + lnx + 8l2n2 + 4l2n2x = 0 + -1lnx + lnx -7ln + lnx + 8l2n2 + 4l2n2x = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -7ln + lnx + 8l2n2 + 4l2n2x = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-7 + x + 8ln + 4lnx) = 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 '(-7 + x + 8ln + 4lnx)' equal to zero and attempt to solve: Simplifying -7 + x + 8ln + 4lnx = 0 Reorder the terms: -7 + 8ln + 4lnx + x = 0 Solving -7 + 8ln + 4lnx + x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 8ln + 4lnx + 7 + x = 0 + 7 Reorder the terms: -7 + 7 + 8ln + 4lnx + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 8ln + 4lnx + x = 0 + 7 8ln + 4lnx + x = 0 + 7 Combine like terms: 0 + 7 = 7 8ln + 4lnx + x = 7 Add '-1x' to each side of the equation. 8ln + 4lnx + x + -1x = 7 + -1x Combine like terms: x + -1x = 0 8ln + 4lnx + 0 = 7 + -1x 8ln + 4lnx = 7 + -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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