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Simplifying ln(4x) = ln(8) + ln(x2) Remove parenthesis around (4x) ln * 4x = ln(8) + ln(x2) Reorder the terms for easier multiplication: 4ln * x = ln(8) + ln(x2) Multiply ln * x 4lnx = ln(8) + ln(x2) Reorder the terms for easier multiplication: 4lnx = 8ln + ln(x2) Multiply ln * x2 4lnx = 8ln + lnx2 Solving 4lnx = 8ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. -8ln + 4lnx = 8ln + -8ln + lnx2 Combine like terms: 8ln + -8ln = 0 -8ln + 4lnx = 0 + lnx2 -8ln + 4lnx = lnx2 Add '-1lnx2' to each side of the equation. -8ln + 4lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -8ln + 4lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + 4x + -1x2) = 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 '(-8 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying -8 + 4x + -1x2 = 0 Solving -8 + 4x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 4x + 8 + -1x2 = 0 + 8 Reorder the terms: -8 + 8 + 4x + -1x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4x + -1x2 = 0 + 8 4x + -1x2 = 0 + 8 Combine like terms: 0 + 8 = 8 4x + -1x2 = 8 Add '-4x' to each side of the equation. 4x + -4x + -1x2 = 8 + -4x Combine like terms: 4x + -4x = 0 0 + -1x2 = 8 + -4x -1x2 = 8 + -4x Add 'x2' to each side of the equation. -1x2 + x2 = 8 + -4x + x2 Combine like terms: -1x2 + x2 = 0 0 = 8 + -4x + x2 Simplifying 0 = 8 + -4x + x2 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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