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Simplifying ln(2x2) + ln(x) = ln(32) + -1ln(x) Remove parenthesis around (2x2) ln * 2x2 + ln(x) = ln(32) + -1ln(x) Reorder the terms for easier multiplication: 2ln * x2 + ln(x) = ln(32) + -1ln(x) Multiply ln * x2 2lnx2 + ln(x) = ln(32) + -1ln(x) Multiply ln * x 2lnx2 + lnx = ln(32) + -1ln(x) Reorder the terms: lnx + 2lnx2 = ln(32) + -1ln(x) Reorder the terms for easier multiplication: lnx + 2lnx2 = 32ln + -1ln(x) Multiply ln * x lnx + 2lnx2 = 32ln + -1lnx Solving lnx + 2lnx2 = 32ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-32ln' to each side of the equation. lnx + -32ln + 2lnx2 = 32ln + -32ln + -1lnx Reorder the terms: -32ln + lnx + 2lnx2 = 32ln + -32ln + -1lnx Combine like terms: 32ln + -32ln = 0 -32ln + lnx + 2lnx2 = 0 + -1lnx -32ln + lnx + 2lnx2 = -1lnx Add 'lnx' to each side of the equation. -32ln + lnx + lnx + 2lnx2 = -1lnx + lnx Combine like terms: lnx + lnx = 2lnx -32ln + 2lnx + 2lnx2 = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -32ln + 2lnx + 2lnx2 = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-16 + x + x2) = 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 '(-16 + x + x2)' equal to zero and attempt to solve: Simplifying -16 + x + x2 = 0 Solving -16 + x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '16' to each side of the equation. -16 + x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + x + x2 = 0 + 16 x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 x + x2 = 16 Add '-1x' to each side of the equation. x + -1x + x2 = 16 + -1x Combine like terms: x + -1x = 0 0 + x2 = 16 + -1x x2 = 16 + -1x Add '-1x2' to each side of the equation. x2 + -1x2 = 16 + -1x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 16 + -1x + -1x2 Simplifying 0 = 16 + -1x + -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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