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Simplifying ln(2x3) + -1ln(x) = ln(16) + ln(x) Remove parenthesis around (2x3) ln * 2x3 + -1ln(x) = ln(16) + ln(x) Reorder the terms for easier multiplication: 2ln * x3 + -1ln(x) = ln(16) + ln(x) Multiply ln * x3 2lnx3 + -1ln(x) = ln(16) + ln(x) Multiply ln * x 2lnx3 + -1lnx = ln(16) + ln(x) Reorder the terms: -1lnx + 2lnx3 = ln(16) + ln(x) Reorder the terms for easier multiplication: -1lnx + 2lnx3 = 16ln + ln(x) Multiply ln * x -1lnx + 2lnx3 = 16ln + lnx Solving -1lnx + 2lnx3 = 16ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-16ln' to each side of the equation. -1lnx + -16ln + 2lnx3 = 16ln + -16ln + lnx Reorder the terms: -16ln + -1lnx + 2lnx3 = 16ln + -16ln + lnx Combine like terms: 16ln + -16ln = 0 -16ln + -1lnx + 2lnx3 = 0 + lnx -16ln + -1lnx + 2lnx3 = lnx Add '-1lnx' to each side of the equation. -16ln + -1lnx + -1lnx + 2lnx3 = lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx -16ln + -2lnx + 2lnx3 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -16ln + -2lnx + 2lnx3 = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-8 + -1x + x3) = 0 Ignore the factor 2.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 '(-8 + -1x + x3)' equal to zero and attempt to solve: Simplifying -8 + -1x + x3 = 0 Solving -8 + -1x + x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + -1x + 8 + x3 = 0 + 8 Reorder the terms: -8 + 8 + -1x + x3 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x + x3 = 0 + 8 -1x + x3 = 0 + 8 Combine like terms: 0 + 8 = 8 -1x + x3 = 8 Add 'x' to each side of the equation. -1x + x + x3 = 8 + x Combine like terms: -1x + x = 0 0 + x3 = 8 + x x3 = 8 + x Add '-1x3' to each side of the equation. x3 + -1x3 = 8 + x + -1x3 Combine like terms: x3 + -1x3 = 0 0 = 8 + x + -1x3 Simplifying 0 = 8 + x + -1x3 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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